| [1] | K. Abdel-Malek and Harn-Jou Yeh. On the determination of starting
points for parametric surface intersections. Computer-aided Design
, 29(1):21-35, 1997. BibTeX entry |
| [2] | N. N. Abdelmalek. On the solutions of the linear least squares problems
and pseudo-inverses. Computing, 13(3-4):215-228, 1974. BibTeX entry |
| [3] | V. M. Adukov. Generalized inversion of block Toeplitz matrices.
Linear Algebra and its Applications, 274:85-124, 1998. BibTeX entry |
| [4] | V. M. Adukov. Generalized inversion of finite rank Hankel and Toeplitz
operators with rational matrix symbols. Linear Algebra and its Applications
, 290(1-3):119-134, 1999. BibTeX entry |
| [5] | S. N. Afriat. On the latent vectors and characteristic values of
products of pairs of symmetric idempotents. Quart. J. Math. Oxford
Ser. (2), 7:76-78, 1956. BibTeX entry |
| [6] | S. N. Afriat. Orthogonal and oblique projectors and the characteristics
of pairs of vector spaces. Proc. Cambridge Philos. Soc., 53:800-816,
1957. BibTeX entry |
| [7] | J. H. Ahlberg, E. N. Nilson, and J. L. Walsh. The Theory of Splines
and their Applications. Academic Press, New York, 1967. BibTeX entry |
| [8] | A. C. Aitken. On least squares and linear combinations of observations.
Proceedings of the Royal Society of Edinburgh, Sec A, 55:42-47,
1934. BibTeX entry |
| [9] | Y. Akatsuka and T. Matsuo. Optimal control of linear discrete systems
using the generalized inverse of a matrix. Techn Rept. 13, Institute
of Automatic Control, Nagoya Univ., Nagoya, Japan, 1965. BibTeX entry |
| [10] | F. Akdeniz. A note concerning the Gauss-Markov theorem. J. Fac.
Sci. Karadeniz Tech. Univ., 1:129-133, 1977. BibTeX entry |
| [11] | F. Akdeniz and M. Sweilem. An application of the generalized inverse
to the two way classification for estimating variance components.
J. Karadeniz Univ. Fac. Arts Sci. Ser. Math.-Phys., 9:1-10, 1986.
(extension of [1738]
). BibTeX entry |
| [12] | I. S. Alalouf and G. P. H. Styan. Characterizations of estimability
in the general linear model. Ann. Statist., 7(1):194-200, 1979. BibTeX entry |
| [13] | I. S. Alalouf and G. P. H. Styan. Estimability and testability in
restricted linear models. Math. Operationsforsch. Statist. Ser. Statist.
, 10(2):189-201, 1979. BibTeX entry |
| [14] | A. Albert. Conditions for positive and nonnegative definiteness in
terms of pseudo-inverses. SIAM J. Appl. Math., 17:434-440, 1969. BibTeX entry |
| [15] | A. Albert. Regression and the Moore-Penrose Pseudoinverse.
Academic Press, New York, 1972. BibTeX entry |
| [16] | A. Albert. The Gauss-Markov theorem for regression models with possibly
singular covariances. SIAM J. Appl. Math., 24:182-187, 1973. BibTeX entry |
| [17] | A. Albert. Statistical applications of the pseudo inverse. In Nashed
[1402]
, pages 525-548. BibTeX entry |
| [18] | A. Albert and R. W. Sittler. A method for computing least squares
estimators that keep up with the data. SIAM J. Control, 3:384-417,
1965. BibTeX entry |
| [19] | V. Aleksic and V. Rakocevic. Approximate properties of the Moore-Penrose
inverse. In VIII Conference on Applied Mathematics (Tivat, 1993)
. Univ. Montenegro, Podgorica, 1994, pp. 1-14. BibTeX entry |
| [20] | B. A. Aliev. The pseudo-inverse operator for the product of two operators.
Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet., (2):11-15,
70, 1979. BibTeX entry |
| [21] | M. F. Allam and M. A. Laughton. The use of pseudo and oblique pseudo-inverse
matrices in power system state estimation algorithms. Internat. J.
Control, 24(5):661-671, 1976. BibTeX entry |
| [22] | E. L. Allgower, K. Böhmer, A. Hoy, and V. Janovsky. Direct methods
for solving singular nonlinear equations. ZAMM Z. Angew. Math. Mech.
, 79:219-231, 1999. BibTeX entry |
| [23] | E. L. Allgower and K. Georg. Numerical path following. In Handbook
of Numerical Analysis, Vol. V, pages 3-207. North-Holland, Amsterdam,
1997. BibTeX entry |
| [24] | D. Alpay, J. A. Ball, and V. Bolotnikov. On the bitangential interpolation
problem for contractive valued functions in the polydisk. J. Operator
Theory, 44(2):277-301, 2000. BibTeX entry |
| [25] | D. Alpay, V. Bolotnikov, and Ph. Loubaton. One two-sided residue
interpolation for matrix-valued H 2-functions with symmetries.
J. Math. Anal. Appl., 200(1):76-105, 1996. BibTeX entry |
| [26] | D. Alpay, V. Bolotnikov, and L. Rodman. Two-sided tangential interpolation
for Hilbert-Schmidt operator functions on polydisks. Operator Theory:
Advances and Applications, 124:21-62, 2001. BibTeX entry |
| [27] | D. Alpay, V. Bolotnikov, and L. Rodman. One-sided tangential interpolation
for operator-valued Hardy functions on polydisks. Integral Equations
Operator Theory, 35(3):253-270, 1999. BibTeX entry |
| [28] | M. Altman. A generalization of Newton's method. Bull. Acad.
Polon. Sci. Ser. Sci. Math. Astronom. Phys., 3:189-193, 1955. BibTeX entry |
| [29] | M. Altman. On a generalization of Newton's method. Bull. Acad.
Polon. Sci. Ser. Sci. Math. Astronom. Phys., 5:789-795, 1957. BibTeX entry |
| [30] | J. K. Amburgey, T. O. Lewis, and T. L. Boullion. On computing generalized
characteristic vectors and values for a rectangular matrix. In Boullion
and Odell [255]
, pages 267-275. BibTeX entry |
| [31] | A. R. Amir-Moéz. Geometry of generalized inverses. Math.
Mag., 43:33-36, 1970. BibTeX entry |
| [32] | A. R. Amir-Moéz. Quasi-singular values of linear transformations.
Rend. Circ. Mat. Palermo (2), 22(3):314-316 (1974), 1973. BibTeX entry |
| [33] | A. R. Amir-Moéz. Geometry of determinants and Grassmann algebras.
Delta (Waukesha), 5(2):71-83, 1975. BibTeX entry |
| [34] | A. R. Amir-Moéz. Extreme Properties of Linear Transformations
. Polygonal Publ. House, Washington, NJ, 1990. BibTeX entry |
| [35] | A. R. Amir-Moéz and R. E. Byerly. Pythagorean theorem in unitary
spaces. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat., 7:85-89,
1996. BibTeX entry |
| [36] | A. R. Amir-Moéz and A. Horn. Singular values of a matrix.
Amer. Math. Monthly, 65:742-748, 1958. BibTeX entry |
| [37] | C. L. Anderson. A Geometric Theory of Pseudoinverses and some Applications
in Statistics. Master's thesis in statistics, Southern Methodist Univ.,
1967. BibTeX entry |
| [38] | R. D. Anderson, H. V. Henderson, F. Pukelsheim, and S. R. Searle.
Best estimation of variance components from balanced data, with arbitrary
kurtosis. Math. Operationsforsch. Statist. Ser. Statist., 15(2):163-176,
1984. BibTeX entry |
| [39] | W. N. Anderson, Jr. Shorted operators. SIAM J. Appl. Math.
, 20:520-525, 1971. BibTeX entry |
| [40] | W. N. Anderson, Jr. and R. J. Duffin. Series and parallel addition
of matrices. SIAM J. Appl. Math., 26:576-594, 1969. (see
[1085]
). BibTeX entry |
| [41] | W. N. Anderson, Jr. and M. Schreiber. The infimum of two projections.
Acta Sci. Math. (Szeged), 33:165-168, 1972. BibTeX entry |
| [42] | W. N. Anderson, Jr. and G. E. Trapp. Shorted operators. II.
SIAM J. Appl. Math., 28:60-71, 1975. (this concept first introduced
by Krein [1088]
). BibTeX entry |
| [43] | W. N. Anderson, Jr. and G. E. Trapp. Inequalities for the parallel
connection of resistive n-port networks. J. Franklin Inst.
, 209(5):305-313, 1975. BibTeX entry |
| [44] | W. N. Anderson, Jr. and G. E. Trapp. Analytic operator functions
and electrical networks. In Campbell [318]
, pages 12-26. BibTeX entry |
| [45] | W. N. Anderson, Jr. and G. E. Trapp. Inverse problems for means of
matrices. SIAM J. Algebraic Discrete Methods, 7(2):188-192, 1986. BibTeX entry |
| [46] | T. Ando. Generalized Schur complements. Linear Algebra and its
Applications, 27:173-186, 1979. BibTeX entry |
| [47] | Mihai Anitescu, Dan I. Coroian, M. Zuhair Nashed, and Florian A. Potra.
Outer inverses and multi-body system simulation. Numer. Funct. Anal.
Optim., 17(7-8):661-678, 1996. BibTeX entry |
| [48] | P. M. Anselone and P. J. Laurent. A general method for the construction
of interpolating or smoothing spline-functions. Numer. Math.,
12:66-82, 1968. BibTeX entry |
| [49] | H. Anton and C. S. Duris. On minimum norm and best approximate solutions
of Av=b in normed spaces. J. Approximation Theory
, 16(3):245-250, 1976. BibTeX entry |
| [50] | A. C. Antoulas. Approximation of linear operators in the 2-norm.
Linear Algebra and its Applications, 278(1-3):309-316, 1998. BibTeX entry |
| [51] | R. C. Archibald. A Semicentennial History of the American Mathematical
Society 1888-1938 (2 volumes). American Mathematical Society, New
York, 1938. BibTeX entry |
| [52] | E. Arghiriade. Sur les matrices qui sont permutables avec leur inverse
généralisée. Atti Accad. Naz. Lincei Rend. Cl.
Sci. Fis. Mat. Natur. Ser. VIII, 35:244-251, 1963. BibTeX entry |
| [53] | E. Arghiriade. Remarques sur l'inverse généralisée
d'un produit de matrices. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis.
Mat. Natur. Ser. VIII, 42:621-625, 1967. BibTeX entry |
| [54] | E. Arghiriade. On the generalized inverse of a product of matrices.
An. Univ. Timisoara Ser. Sti. Mat.-Fiz. No., 5:37-42, 1967. BibTeX entry |
| [55] | E. Arghiriade. Sur quelques équations fonctionnelles de matrices.
Rev. Roumaine Math. Pures Appl., 12:1127-1133, 1967. BibTeX entry |
| [56] | E. Arghiriade. Sur l'inverse généralisée d'un
operateur lineaire dans les espaces de Hilbert. Atti Accad. Naz. Lincei
Rend. Cl. Sci. Fis. Mat. Natur. Ser. VIII, 45:471-477, 1968. BibTeX entry |
| [57] | E. Arghiriade and A. Dragomir. Une nouvelle définition de
l'inverse généralisée d'une matrice. Atti Accad.
Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8), 35:158-165, 1963. BibTeX entry |
| [58] | E. Arghiriade and A. Dragomir. Remarques sur quelques théoremes
relatives a l'inverse généralisée d'un operateur lineaire
dans les espaces de hilbert. Atti Accad. Naz. Lincei Rend. Cl. Sci.
Fis. Mat. Natur. Ser. VIII, 46:333-338, 1969. BibTeX entry |
| [59] | I. K. Argyros. Local convergence theorems of Newton's method for
nonlinear equations using outer or generalized inverses. Czechoslovak
Math. J., 50(125)(3):603-614, 2000. BibTeX entry |
| [60] | S. Aronowitz and B. E. Eichinger. Petrie matrices and generalized
inverses. J. Math. Phys., 16:1278-1283, 1975. BibTeX entry |
| [61] | N. Aronszajn. Theory of reproducing kernels. Trans. Amer. Math.
Soc., 68:337-404, 1950. BibTeX entry |
| [62] | F. V. Atkinson. The normal solvability of linear equations in normed
spaces (russian). Mat. Sbornik N.S., 28(70):3-14, 1951. BibTeX entry |
| [63] | F. V. Atkinson. On relatively regular operators. Acta Sci. Math.
Szeged, 15:38-56, 1953. BibTeX entry |
| [64] | K. E. Atkinson. The solution of non-unique linear integral equations.
Numer. Math., 10:117-124, 1967. (see also
[1368]
). BibTeX entry |
| [65] | L. Autonne. Sur les groupes linéaires, réels et orthogonaux.
Bull. Soc. Math. France, 30:121-134, 1902. BibTeX entry |
| [66] | L. Autonne. Sur les matrices hypohermitiennes et sur les matrices
unitaires. Ann. Univ. Lyon, Nouvelle Sér. I, 38:1-77, 1915.
(see history of SVD in [1771]
). BibTeX entry |
| [67] | K. E. Avrachenkov, M. Haviv, and P. G. Howlett. Inversion of analytic
matrix functions that are singular at the origin. SIAM J. Matrix Anal.
Appl., 22(4):1175-1189 (electronic), 2001. BibTeX entry |
| [68] | Gorô Azumaya. Strongly pi-regular rings. J. Fac.
Sci. Hokkaido Univ. Ser. I., 13:34-39, 1954. BibTeX entry |
| [69] | G. Backus. Inference from inadequate and inaccurate data. I, II.
Proc. Nat. Acad. Sci. U.S.A. 65 (1970), 1-7; ibid., 65:281-287,
1970. BibTeX entry |
| [70] | G. Backus and F. Gilbert. Uniqueness in the inversion of inaccurate
gross Earth data. Philos. Trans. Roy. Soc. London Ser. A, 266(1173):123-192,
1970. BibTeX entry |
| [71] | C. Badea and M. Mbekhta. Generalized inverses and the maximal radius
of regularity of a Fredholm operator. Integral Equations Operator
Theory, 28(2):133-146, 1997. BibTeX entry |
| [72] | C. Badea and M. Mbekhta. Compressions of resolvents and maximal radius
of regularity. Trans. Amer. Math. Soc., 351(7):2949-2960, 1999. BibTeX entry |
| [73] | J. K. Baksalary. A relationship between the star and minus orderings.
Linear Algebra and its Applications, 82:163-167, 1986. BibTeX entry |
| [74] | J. K. Baksalary and O. M. Baksalary. Commutativity of projectors.
Linear Algebra and its Applications, 341:129-142, 2002. BibTeX entry |
| [75] | J. K. Baksalary and J. Hauke. Partial orderings of matrices referring
to singular values or eigenvalues. Linear Algebra and its Applications
, 96:17-26, 1987. BibTeX entry |
| [76] | J. K. Baksalary and R. Kala. The matrix equation AX
-YB=C. Linear Algebra and its Applications,
25:41-43, 1979. BibTeX entry |
| [77] | J. K. Baksalary and R. Kala. The matrix equation AX
B+CYD=E. Linear Algebra and its Applications
, 30:141-147, 1980. BibTeX entry |
| [78] | J. K. Baksalary and R. Kala. Two properties of a nonnegative definite
matrix. Bull. Acad. Polon. Sci. Sér. Sci. Math., 28(5-6):233-235
(1981), 1980. BibTeX entry |
| [79] | J. K. Baksalary and R. Kala. Range invariance of certain matrix products.
Linear and Multilinear Algebra, 14(1):89-96, 1983. BibTeX entry |
| [80] | J. K. Baksalary and R. Kala. Corrigendum: ``On equalities between
BLUEs, WLSEs, and SLSEs''. Canad. J. Statist., 12(3):240, 1984. BibTeX entry |
| [81] | J. K. Baksalary and R. Kala. On equalities between BLUEs, WLSEs,
and SLSEs. Canad. J. Statist., 11(2):119-123, 1983. (extension
of [1203]
). BibTeX entry |
| [82] | J. K. Baksalary and T. Mathew. Rank invariance criterion and its
application to the unified theory of least squares. Linear Algebra
and its Applications, 127:393-401, 1990. BibTeX entry |
| [83] | J. K. Baksalary and S. K. Mitra. Left-star and right-star partial
orderings. Linear Algebra and its Applications, 149:73-89, 1991. BibTeX entry |
| [84] | J. K. Baksalary, P. R. Pordzik, and G. Trenkler. A note on generalized
ridge estimators. Comm. Statist. Theory Methods, 19(8):2871-2877,
1990. BibTeX entry |
| [85] | J. K. Baksalary and F. Pukelsheim. On the Löwner, minus, and
star partial orderings of nonnegative definite matrices and their squares.
Linear Algebra and its Applications, 151:135-141, 1991. BibTeX entry |
| [86] | J. K. Baksalary, S. Puntanen, and H. Yanai. Canonical correlations
associated with symmetric reflexive generalized inverses of the dispersion
matrix. Linear Algebra and its Applications, 176:61-74, 1992. BibTeX entry |
| [87] | J. K. Baksalary, F. Pukelsheim, and G. P. H. Styan. Some properties
of matrix partial orderings. Linear Algebra and its Applications
, 119:57-85, 1989. BibTeX entry |
| [88] | J. K. Baksalary, P. Semrl, and G. P. H. Styan. A note on rank-aditivity
and range-aditivity. Linear Algebra and its Applications, 237-238:489-498,
1996. BibTeX entry |
| [89] | A. V. Balakrishnan. An operator theoretic formulation of a class
of control problems and a steepest descent method of solution. J.
Soc. Indust. Appl. Math. Ser. A: Control, 1:109-127, 1963. BibTeX entry |
| [90] | K. F. Baldwin and A. E. Hoerl. Bounds of minimum mean squared error
in ridge regression. Comm. Statist. A-Theory Methods, 7(13):1209-1218,
1978. BibTeX entry |
| [91] | J. A. Ball, M. Rakowski, and B. F. Wyman. Coupling operators, Wedderburn-Forney
spaces, and generalized inverses. Linear Algebra and its Applications
, 203/204:111-138, 1994. BibTeX entry |
| [92] | K. S. Banerjee. Singularity in Hotelling's weighing designs and generalized
inverses. Ann. Math. Statist., 37:1021-1032, 1966. (erratum,
ibid 40(1969), 710). BibTeX entry |
| [93] | K. S. Banerjee and W. T. Federer. On the structure and analysis of
singular fractional replicates. Ann. Math. Statist., 39:657-663,
1968. BibTeX entry |
| [94] | R. B. Bapat. Generalized inverses with proportional minors.
Linear Algebra and its Applications, 211:27-33, 1994. BibTeX entry |
| [95] | R. B. Bapat. Moore-Penrose inverse of the incidence matrix of a tree.
Linear and Multilinear Algebra, 42(2):159-167, 1997. BibTeX entry |
| [96] | R. B. Bapat. Structure of a nonnegative regular matrix and its generalized
inverses. Linear Algebra and its Applications, 268:31-39, 1998. BibTeX entry |
| [97] | R. B. Bapat. Linear estimation in models based on a graph. Linear
Algebra and its Applications, 302/303:223-230, 1999. BibTeX entry |
| [98] | R. B. Bapat. Resistance distance in graphs. Mathematics Student
, 68:87-98, 1999. BibTeX entry |
| [99] | R. B. Bapat. Linear Algebra and Linear Models. Hindustan
Book Agency, New Delhi, second edition, 1999. BibTeX entry |
| [100] | R. B. Bapat. Moore-Penrose inverse of set inclusion matrices.
Linear Algebra and its Applications, 318(1-3):35-44, 2000. BibTeX entry |
| [101] | R. B. Bapat. Outer inverses: Jacobi type identities and nullities
of submatrices. To appear, 2002. BibTeX entry |
| [102] | R. B. Bapat and A. Ben-Israel. Singular values and maximum rank minors
of generalized inverses. Linear and Multilinear Algebra, 40(2):153-161,
1995. BibTeX entry |
| [103] | R. B. Bapat and R. E. Hartwig. A master of the row space and the
column space: the mathematical work of Sujit Kumar Mitra. In Bapat et
al. [108]
, pages 5-14. (special issue of Linear Algebra and its Applications
211 (1994)). BibTeX entry |
| [104] | R. B. Bapat, S. K. Jain, and S. Pati. Weighted Moore-Penrose inverse
of a Boolean matrix. Linear Algebra and its Applications, 255:267-279,
1997. BibTeX entry |
| [105] | R. B. Bapat, S. K. Jain, and K. M. Prasad. Generalized power symmetric
stochastic matrices. Proc. Amer. Math. Soc., 127(7):1987-1994, 1999. BibTeX entry |
| [106] | R. B. Bapat, S. K. Jain, and L. E. Snyder. Nonnegative idempotent
matrices and the minus partial order. Linear Algebra and its Applications
, 261:143-154, 1997. BibTeX entry |
| [107] | R. B. Bapat and D. M. Kulkarni. Minors of some matrices associated
with a tree. In Algebra and Its Applications. Contemporary Mathematics
259 (D. V. Huynh, S. K. Jain, S. R. Lopez-Permouth Ed.), pages 45-66.
American Math Society, Providence, RI, 2000. BibTeX entry |
| [108] | R. B. Bapat, S. K. Mitra, and R. Hartwig, editors. Generalized
Inverses. Papers from the Workshop on g-inverses held in Calcutta,
December 11-16, 1993, New York, 1994. North-Holland Publishing Co.
(special issue of Linear Algebra and its Applications 211
(1994)). BibTeX entry |
| [109] | R. B. Bapat and Sukanta Pati. Algebraic connectivity and the characteristic
set of a graph. Linear and Multilinear Algebra, 45(2-3):247-273,
1998. BibTeX entry |
| [110] | R. B. Bapat and K. M. Prasad. Cochran's theorem and related results
on matrix rank over a commutative ring. In Statistical Inference and
Design of Experiments (U. J. Dixit and M. R. Satam Ed.), pages 125-133.
Narosa Publishing House, 1999. BibTeX entry |
| [111] | R. B. Bapat and T. E. S. Raghavan. Nonnegative Matrices and Applications
. Cambridge University Press, Cambridge, 1997. BibTeX entry |
| [112] | R. B. Bapat, K. P. S. Bhaskara Rao, and K. M. Prasad. Generalized
inverses over integral domains. Linear Algebra and its Applications
, 140:181-196, 1990. BibTeX entry |
| [113] | R. B. Bapat and D. W. Robinson. The Moore-Penrose inverse over a
commutative ring. Linear Algebra and its Applications, 177:89-103,
1992. BibTeX entry |
| [114] | G. P. Barker and S. L. Campbell. Internal stability of two-dimensional
systems. Linear and Multilinear Algebra, 14(4):365-369, 1983. BibTeX entry |
| [115] | G. A. Barnard. The logic of least squares. J. Roy. Statist.
Soc. Ser. B, 25:124-127, 1963. BibTeX entry |
| [116] | S. Barnett. Matrices in Control Theory. Van Nostrand Reinhold,
London, 1971. BibTeX entry |
| [117] | S. Barnett. Matrices: Methods and Applications. Clarendon
Press, Oxford, 1990. BibTeX entry |
| [118] | H. Bart, M. A. Kaashoek, and D. C. Lay. Relative inverses of meromorphic
operator functions and associated holomorphic projection functions.
Math. Ann., 218(3):199-210, 1975. BibTeX entry |
| [119] | G. Basile. Alcune osservazioni sulla pseudoinversa di una matrice
rettangolare. Atti Accad. Sci. Ist. Bologna Cl. Sci. Fis. Rend. (12)
, 6(fasc.):1-2, 236-240, 1968/1969. BibTeX entry |
| [120] | T. S. Baskett and I. J. Katz. Theorems on products of E
Pr matrices. Linear Algebra and its Applications, 2:87-103,
1969. BibTeX entry |
| [121] | H. Bateman. A formula for the solving function of a certain integral
equation of the second kind. Transactions of the Cambridge Philosophical
Society, 20:179-187, 1908. BibTeX entry |
| [122] | H. Bateman. The reality of the roots of certain transcendental equations
occurring in the theory of integral equations. Transactions of the
Cambridge Philosophical Society, 20:371-381, 1908. BibTeX entry |
| [123] | H. Bateman. On the application of integral equations to the determination
of upper and lower limits of a double integral. Transactions of the
Cambridge Philosophical Society, 21:123-128, 1908. BibTeX entry |
| [124] | H. Bateman. On the numerical solution of linear integral equations.
Proc. Roy. Soc. London Ser. A, 100:441-449, 1922. BibTeX entry |
| [125] | D. Batigne. Integral generalized inverses of integral matrices.
Linear Algebra and its Applications, 22:125-134, 1978. BibTeX entry |
| [126] | D. R. Batigne, F. J. Hall, and I. J. Katz. Further results on integral
generalized inverses of integral matrices. Linear and Multilinear
Algebra, 6(3):233-241, 1978/79. BibTeX entry |
| [127] | F. L. Bauer. A further generalization of the Kantorovic inequality.
Numer. Math., 3:117-119, 1961. BibTeX entry |
| [128] | F. L. Bauer. Elimination with weighted row combinations for solving
linear equations and least squares problems. Numer. Math., 7:338-352,
1965. (republished, pp. 119-133 in [2058]
). BibTeX entry |
| [129] | F. L. Bauer. Theory of norms. Computer Science Dept. CS 75, Stanford
University, Stanford, 1967. BibTeX entry |
| [130] | F. L. Bauer, J. Stoer, and C. Witzgall. Absolute and monotonic norms.
Numer. Math., 3:257-264, 1961. BibTeX entry |
| [131] | E. F. Beckenbach and R. Bellman. Inequalities. Springer-Verlag,
New York, 3rd edition, 1971. BibTeX entry |
| [132] | R. Bellman. Introduction to Matrix Analysis. McGraw-Hill
Book Co., New York, 2nd edition, 1970. BibTeX entry |
| [133] | E. Beltrami. Sulle funzioni bilineari. Giornale di Matematiche
ad Uso degli Studenti Delle Universita, 11:98-106, 1873. (an English
translation by D. Boley is available as University of Minnesota, Department
of Computer Science, Technical Report 90-37, 1990. see history of SVD in
[1771]
). BibTeX entry |
| [134] | E. J. Beltrami. A constructive proof of the Kuhn-Tucker multiplier
rule. J. Math. Anal. Appl., 26:297-306, 1969. BibTeX entry |
| [135] | A. Ben-Israel. On direct sum decompositions of Hestenes algebras.
Israel J. Math., 2:50-54, 1964. BibTeX entry |
| [136] | A. Ben-Israel. An iterative method for computing the generalized
inverse of an arbitrary matrix. Math. Comput., 19:452-455, 1965. BibTeX entry |
| [137] | A. Ben-Israel. A modified Newton-Raphson method for the solution
of systems of equations. Israel J. Math., 3:94-98, 1965. BibTeX entry |
| [138] | A. Ben-Israel. On error bounds for generalized inverses. SIAM
J. Numer. Anal., 3:585-592, 1966. (see also [1765]
). BibTeX entry |
| [139] | A. Ben-Israel. A Newton-Raphson method for the solution of systems
of equations. J. Math. Anal. Appl., 15:243-252, 1966. BibTeX entry |
| [140] | A. Ben-Israel. A note on the Cayley transform. Notices Amer.
Math. Soc., 13:599, 1966. BibTeX entry |
| [141] | A. Ben-Israel. A note on an iterative method for generalized inversion
of matrices. Math. Comput., 20:439-440, 1966. BibTeX entry |
| [142] | A. Ben-Israel. On the geometry of subspaces in Euclidean n
-spaces. SIAM J. Appl. Math., 15:1184-1198, 1967. BibTeX entry |
| [143] | A. Ben-Israel. On iterative methods for solving nonlinear least squares
problems over convex sets. Israel J. Math., 5:211-214, 1967. BibTeX entry |
| [144] | A. Ben-Israel. On applications of generalized inverses in nonlinear
analysis. In Boullion and Odell [255]
, pages 183-202. BibTeX entry |
| [145] | A. Ben-Israel. On decompositions of matrix spaces with applications
to matrix equations. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat.
Natur. (8), 45:122-128, 1968. BibTeX entry |
| [146] | A. Ben-Israel. On optimal solutions of 2-person 0-sum games.
Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8), 44:512-516,
1968. BibTeX entry |
| [147] | A. Ben-Israel. On matrices of index zero or one. SIAM J. Appl.
Math., 17:1118-1121, 1969. (see [1281]
, [1636]
). BibTeX entry |
| [148] | A. Ben-Israel. A note on partitioned matrices and equations.
SIAM Rev., 11:247-250, 1969. BibTeX entry |
| [149] | A. Ben-Israel. On Newton's method in nonlinear programming. In
Kuhn [1098]
, pages 339-352. BibTeX entry |
| [150] | A. Ben-Israel. Applications of generalized inverses to programming,
games, and networks. In Nashed [1402]
, pages 495-523. BibTeX entry |
| [151] | A. Ben-Israel. A Cramer rule for least-norm solutions of consistent
linear equations. Linear Algebra and its Applications, 43:223-226,
1982. (see [1912]
, [373]
, [374]
, [375]
, [1787]
, [1926]
, [1931]
, [2032]
). BibTeX entry |
| [152] | A. Ben-Israel. Generalized inverses of matrices: a perspective of
the work of Penrose. Math. Proc. Cambridge Philos. Soc., 100(3):407-425,
1986. BibTeX entry |
| [153] | A. Ben-Israel. A volume associated with m× n
matrices. Linear Algebra and its Applications, 167:87-111, 1992.
(this concept was introduced by Good [687]
). BibTeX entry |
| [154] | A. Ben-Israel. The change-of-variables formula using matrix volume.
SIAM J. Matrix Anal. Appl., 21(1):300-312 (electronic), 1999. BibTeX entry , http://epubs.siam.org/sam%2Dbin/pii.pl?pii=S0895479895296896 |
| [155] | A. Ben-Israel. A local inverse for nonlinear mappings. Numer.
Algorithms, 25(1-4):37-46, 2000. Mathematical journey through analysis,
matrix theory and scientific computation (Kent, OH, 1999). BibTeX entry |
| [156] | A. Ben-Israel. An application of the matrix volume in probability.
Linear Algebra and its Applications, 321:9-25, 2001. BibTeX entry |
| [157] | A. Ben-Israel. The Moore of the Moore-Penrose inverse. To appear
, 2002. BibTeX entry |
| [158] | A. Ben-Israel and A. Charnes. Contributions to the theory of generalized
inverses. J. Soc. Indust. Appl. Math., 11:667-699, 1963. BibTeX entry |
| [159] | A. Ben-Israel and A. Charnes. Generalized inverses and the Bott-Duffin
network analysis. J. Math. Anal. Appl., 7:428-435, 1963. (corrigendum
in J. Math. Anal. Appl. 18(1967), 393). BibTeX entry |
| [160] | A. Ben-Israel and A. Charnes. An explicit solution of a special class
of linear programming problems. Operations Res., 16:1166-1175,
1968. (see [181]
, [209]
, [1601]
, [1646]
). BibTeX entry |
| [161] | A. Ben-Israel, A. Charnes, and P. D. Robers. On generalized inverses
and interval linear programming. In Boullion and Odell
[255]
, pages 53-70. BibTeX entry |
| [162] | A. Ben-Israel and D. Cohen. On iterative computation of generalized
inverses and associated projections. SIAM J. Numer. Anal., 3:410-419,
1966. BibTeX entry |
| [163] | A. Ben-Israel and T. N. E. Greville. Generalized Inverses: Theory
and Applications. Wiley-Interscience [John Wiley & Sons], New York,
1974. (reprinted by Robert E. Krieger Publishing Co. Inc., Huntington,
NY, 1980.). BibTeX entry |
| [164] | A. Ben-Israel and T. N. E. Greville. Some topics in generalized inverses
of matrices. In Nashed [1402]
, pages 125-147. BibTeX entry |
| [165] | A. Ben-Israel and M. J. L. Kirby. A characterization of equilibrium
points of bimatrix games. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis.
Mat. Natur. (8), 46:402-407, 1969. BibTeX entry |
| [166] | A. Ben-Israel and S. J. Wersan. An elimination method for computing
the generalized inverse of an arbitrary complex matrix. J. Assoc.
Comput. Mach., 10:532-537, 1963. BibTeX entry |
| [167] | J. M. Bennett and J. J. Edwards. A graph isomorphism algorithm using
pseudoinverses. BIT, 36(1):41-53, 1996. BibTeX entry |
| [168] | M. W. Benson and P. O. Frederickson. Fast parallel algorithms for
the Moore-Penrose pseudo-inverse. In Hypercube Multiprocessors 1987
(Knoxville, TN, 1986), pages 597-604. SIAM, Philadelphia, PA, 1987. BibTeX entry |
| [169] | M. W. Benson and P. O. Frederickson. Fast pseudo-inverse algorithms
on hypercubes. In Multigrid Methods (Copper Mountain, CO, 1987),
pages 23-33. Dekker, New York, 1988. BibTeX entry |
| [170] | A. Ben-Tal and M. Teboulle. A geometric property of the least squares
solution of linear equations. Linear Algebra and its Applications
, 139:165-170, 1990. (see [177]
, [486]
, [153]
, [171]
, [233]
, [612]
). BibTeX entry |
| [171] | A. Ben-Tal and M. Teboulle. Addenda: ``A geometric property of the
least squares solution of linear equations'' [Linear Algebra Appl. 139
(1990), 165-170]. Linear Algebra and its Applications, 180:5, 1993. BibTeX entry |
| [172] | M. Benzi and C. D. Meyer, Jr. A direct projection method for sparse
linear systems. SIAM J. Sci. Comput., 16(5):1159-1176, 1995. BibTeX entry |
| [173] | H. Berens and M. Finzel. A continuous selection of the metric projection
in matrix spaces. In Numerical Methods of Approximation Theory, Vol.
8 (Oberwolfach, 1986), pages 21-29. Birkhäuser, Basel, 1987.
(see [174]
). BibTeX entry |
| [174] | H. Berens and M. Finzel. Addendum: ``A continuous selection of the
metric projection in matrix spaces'' [in numerical methods of approximation
theory, vol. 8 (Oberwolfach, 1986), 21-29, Birkhäuser, Basel,
1987; MR 90i:41040]. Numer. Math., 57(6-7):663-667, 1990. BibTeX entry |
| [175] | I.S. Berezin and N.P. Zhidkov. Computing Methods. Pergamon
Press, London, 1965. BibTeX entry |
| [176] | L. Berg. Über quasivertauschbare Matrixinversen. Rostock.
Math. Kolloq., (15):5-10, 1980. BibTeX entry |
| [177] | L. Berg. Three results in connection with inverse matrices.
Linear Algebra and its Applications, 84:63-77, 1986. (see also
[170]
). BibTeX entry |
| [178] | M. Berger and B. Gostiaux. Differential Geometry: Manifolds, Curves
and Surfaces. Graduate Texts in Mathematics No. 115. Springer-Verlag,
New York, 1988. (translated by S. Levy). BibTeX entry |
| [179] | P. G. Bergman, R. Penfield, R. Schiller, and H. Zatkis. The Hamiltonian
of the general theory of relativity with electromagnetic field. Physical
Review, 52:1950, 1950. BibTeX entry |
| [180] | A. Berman. Nonnegative matrices which are equal to their generalized
inverse. Linear Algebra and its Applications, 9:261-265, 1974. BibTeX entry |
| [181] | A. Berman. Generalized interval programming. Bull. Calcutta
Math. Soc., 71(3):169-176, 1979. BibTeX entry |
| [182] | A. Berman and S. K. Jain. Nonnegative generalized inverses of powers
of nonnegative matrices. Linear Algebra and its Applications, 107:169-179,
1988. BibTeX entry |
| [183] | A. Berman and M. Neumann. Proper splittings of rectangular matrices.
SIAM J. Appl. Math., 31(2):307-312, 1976. BibTeX entry |
| [184] | A. Berman and M. Neumann. Consistency and splittings. SIAM J.
Numer. Anal., 13(6):877-888, 1976. BibTeX entry |
| [185] | A. Berman and R. J. Plemmons. Monotonicity and the generalized inverse.
SIAM J. Appl. Math., 22:155-161, 1972. BibTeX entry |
| [186] | A. Berman and R. J. Plemmons. Inverses of nonnegative matrices.
Linear and Multilinear Algebra, 2:161-172, 1974. BibTeX entry |
| [187] | A. Berman and R. J. Plemmons. Cones and iterative methods for best
least squares solutions of linear systems. SIAM J. Numer. Anal.
, 11:145-154, 1974. BibTeX entry |
| [188] | A. Berman and R. J. Plemmons. Nonnegative Matrices in the Mathematical
Sciences. Society for Industrial and Applied Mathematics (SIAM), Philadelphia,
PA, 1994. (revised reprint of the 1979 original). BibTeX entry |
| [189] | L. Bernard. A generalized inverse method for asymptotic linear programming.
Mathematical Programming, 43:71-86, 1989. BibTeX entry |
| [190] | L. Bernard. An efficient basis update for asymptotic linear programming.
Linear Algebra and its Applications, 184:83-102, 1993. BibTeX entry |
| [191] | Kenneth W. Berryman, Mario E. Inchiosa, Arthur M. Jaffe, and Steven
A. Janowsky. Extending the pseudoinverse rule. In Neural Networks
and Spin Glasses (Pôrto Alegre, 1989), pages 169-175. World Sci.
Publishing, Teaneck, NJ, 1990. BibTeX entry |
| [192] | M. Bertero, C. De Mol, and E. R. Pike. Linear inverse problems with
discrete data. I. General formulation and singular system analysis.
Inverse Problems, 1(4):301-330, 1985. BibTeX entry |
| [193] | M. Bertero, C. De Mol, and E. R. Pike. Linear inverse problems with
discrete data. II. Stability and regularisation. Inverse Problems
, 4(3):573-594, 1988. BibTeX entry |
| [194] | J. Bérubé, R. E. Hartwig, and G. P. H. Styan. On canonical
correlations and the degrees of non-orthogonality in the three-way layout.
In Statistical Sciences and Data Analysis (Tokyo, 1991), pages
247-252. VSP, Utrecht, 1993. BibTeX entry |
| [195] | F. J. Beutler. The operator theory of the pseudo-inverse. I. Bounded
operators. J. Math. Anal. Appl., 10:451-470, 1965. BibTeX entry |
| [196] | F. J. Beutler. The operator theory of the pseudo-inverse. II. Unbounded
operators with arbitrary range. J. Math. Anal. Appl., 10:471-493,
1965. BibTeX entry |
| [197] | F. J. Beutler and W. L. Root. The operator pseudoinverse in control
and systems identification. In Nashed [1402]
, pages 397-494. BibTeX entry |
| [198] | J. H. Bevis, F. J. Hall, and I. J. Katz. Integer generalized inverses
of incidence matrices. Linear Algebra and its Applications, 39:247-258,
1981. BibTeX entry |
| [199] | J. H. Bevis, F. J. Hall, and R. E. Hartwig. The Drazin inverse of
a semilinear transformation and its matrix representation. Linear
Algebra and its Applications, 97:229-242, 1987. BibTeX entry |
| [200] | J. H. Bevis, F. J. Hall, and R. E. Hartwig. Consimilarity and the
matrix equation A X-XB=C. In Current
Trends in Matrix Theory (Auburn, Ala., 1986), pages 51-64. North-Holland,
New York, 1987. BibTeX entry |
| [201] | R. Bhatia. Perturbation Bounds for Matrix Eigenvalues. Longman
Scientific & Technical, Harlow, 1987. BibTeX entry |
| [202] | R. Bhatia. Letter to the editor: ``The n-dimensional Pythagorean
theorem'' [Linear and Multilinear Algebra 26(1990), no. 1-2, 9-13;
MR 90k:51031] by S.-Y. T. Lin and Y. F. Lin. Linear and Multilinear
Algebra, 30(1-2):155, 1991. (see [1176]
). BibTeX entry |
| [203] | R. Bhatia. Matrix Analysis. Springer-Verlag, New York, 1997. BibTeX entry |
| [204] | P. Bhimasankaram. A characterization of subclasses of generalized
inverses of specified rank. Sankhya Ser. A, 36(2):214-218, 1974. BibTeX entry |
| [205] | P. Bhimasankaram. On generalized inverses of a block in a partitioned
matrix. Linear Algebra and its Applications, 109:131-143, 1988. BibTeX entry |
| [206] | P. Bhimasankaram. Rank factorization of a matrix and its applications.
Math. Sci., 13(1):4-14, 1988. (see [1591]
). BibTeX entry |
| [207] | P. Bhimasankaram and T. Mathew. On ordering properties of generalized
inverses of nonnegative definite matrices. Linear Algebra and its
Applications, 183:131-146, 1993. BibTeX entry |
| [208] | P. Bhimasankaram and R. SahaRay. On a partitioned linear model and
some associated reduced models. Linear Algebra and its Applications
, 264:329-339, 1997. BibTeX entry |
| [209] | M. Bilodeau. Sur une représentation explicite des solutions
optimales d'un programme linéaire. Canad. Math. Bull.,
29(4):419-425, 1986. BibTeX entry |
| [210] | G. D. Birkhoff. Review of ``The New Haven Colloquium. by E. H. Moore,
E. J. Wilczynski, M. Mason. Yale University Press, 1910, x + 222 p.''.
Bull. Amer. Math. Soc., 17:414-428, 1911. BibTeX entry |
| [211] | Z. W. Birnbaum. Introduction to Probability and Mathematical Statistics
. Harper & Brothers, Publishers, New York, 1962. BibTeX entry |
| [212] | A. Bjerhammar. Rectangular reciprocal matrices, with special reference
to geodetic calculations. Bull. Géodésique, pages
188-220, 1951. BibTeX entry |
| [213] | A. Bjerhammar. Application of calculus of matrices to method of least
squares with special reference to geodetic calculations. Trans. Roy.
Inst. Tech. Stockholm, 1951(49):86 pp. (2 plates), 1951. BibTeX entry |
| [214] | A. Bjerhammar. A generalized matrix algebra. Trans. Roy. Inst.
Tech. Stockholm, 1958(124):32 pp., 1958. BibTeX entry |
| [215] | A. Bjerhammar. Studies with generalized matrix algebra. Bull.
Géodésique (N.S.) No., 85:193-210, 1967. BibTeX entry |
| [216] | A. Bjerhammar. Theory of Errors and Generalized Matrix Inverses
. Elsevier Scientific Publishing Co., Amsterdam, 1973. BibTeX entry |
| [217] | Å. Björck. Solving linear least squares problems by Gram-Schmidt
orthogonalization. BIT, 7:1-21, 1967. BibTeX entry |
| [218] | Å. Björck. Iterative refinement of linear least squares
solutions I. BIT, 7:257-278, 1967. BibTeX entry |
| [219] | Å. Björck. Iterative refinement of linear least squares
solutions II. BIT, 8:8-30, 1968. BibTeX entry |
| [220] | Å. Björck. A uniform numerical method for linear estimation
from general Gauss-Markov models. In Proceedings of the First Symposium
on Comutational Statistics (COMPSTAT), (G. Bruckmann, F. Ferschl and L.
Schmetterer, Editors), pages 131-140. Physica Verlag, Vienna, 1974. BibTeX entry |
| [221] | Å. Björck. Numerical Methods for Least Squares Problems
. Society for Industrial and Applied Mathematics (SIAM), Philadelphia,
PA, 1994. BibTeX entry |
| [222] | Å. Björck and C. Bowie. An iterative algorithm for computing
the best estimate of an orthogonal matrix. SIAJN, 8(2):358-364,
1971. BibTeX entry |
| [223] | Å. Björck and T. Elfving. Accelerated projection methods
for computing pseudoinverse solutions of systems of linear equations.
BIT, 19:145-163, 1979. BibTeX entry |
| [224] | Å. Björck and G. H. Golub. Iterative refinement of linear
least squares solutions by householder transformation. BIT, 7:322-337,
1967. BibTeX entry |
| [225] | Å. Björck and G. H. Golub. Numerical methods for computing
angles between linear subspaces. Mathematics of Computation, 27:579-594,
1973. BibTeX entry |
| [226] | B. Blaschke, A. Neubauer, and O. Scherzer. On convergence rates for
the iteratively regularized Gauss-Newton method. IMA J. Numer. Anal.
, 17(3):421-436, 1997. BibTeX entry |
| [227] | J. Blatter and E. W. Cheney. On the existence of extremal projections.
J. Approximation Theory, 6:72-79, 1972. BibTeX entry |
| [228] | J. W. Blattner. Bordered matrices. J. Soc. Indust. Appl. Math.
, 10:528-536, 1962. BibTeX entry |
| [229] | J. W. Blattner. On the convergence of a certain matrix iteration.
Bul. Inst. Politehn. Iasi (N.S.), 10 (14)(3-4):43-46, 1964. BibTeX entry |
| [230] | G. A. Bliss. Eliakim Hastings Moore. Bull. Amer. Math. Soc.
, 39:831-838, 1933. BibTeX entry |
| [231] | G. A. Bliss. The scientific work of Eliakim Hastings Moore.
Bull. Amer. Math. Soc., 40:501-514, 1934. BibTeX entry |
| [232] | L. Bober and P. Chrzan. Application of the generalized Moore-Penrose
matrix inversion to the estimation of a classical econometric model under
additional constraints. Przegl# ad Statyst., 25(3):315-324 (1979),
1978. BibTeX entry |
| [233] | E. Y. Bobrovnikova and S. A. Vavasis. A norm bound for projections
with complex weights. Linear Algebra and its Applications, 307(1-3):69-75,
2000. (a complex version of the bounds in [1770]
, [1852]
). BibTeX entry |
| [234] | P. T. Boggs. The convergence of the Ben-Israel iteration for nonlinear
least squares problems. Math. Comp., 30(135):512-522, 1976. BibTeX entry |
| [235] | E. Bohl and P. Lancaster. Perturbation of spectral inverses applied
to a boundary layer phenomenon arising in chemical networks. Linear
Algebra and its Applications, 180:35-59, 1993. BibTeX entry |
| [236] | E. Boman and I. Koltracht. Computing preconditioners via subspace
projection. Linear Algebra and its Applications, 302/303:347-353,
1999. BibTeX entry |
| [237] | F. Bohnenblust. A characterization of complex Hilbert spaces.
Portugal. Math., 3:103-109, 1942. BibTeX entry |
| [238] | T. Bonnesen and W. Fenchel. Theorie der konvexen Körper
. Springer, Berlin, 1934. BibTeX entry |
| [239] | C. de Boor. The Method of Projections as applied to the Numerical
Solution of Two Point Boundary Value Problems using Cubic Splines
. Doctoral dissertation in mathematics, University of Michigan, Ann Arbor,
MI, 1966. BibTeX entry |
| [240] | C. de Boor. Convergence of abstract splines. J. Approx. Theory
, 31(1):80-89, 1981. BibTeX entry |
| [241] | J. C. G. Boot. The computation of the generalized inverse of singular
or rectangular matrices. Amer. Math. Monthly, 70:302-303, 1963. BibTeX entry |
| [242] | E. Boros. On the generalized inverse of an EPr
matrix. An. Univ. Timisoara Ser. Sti. Mat.-Fiz. No., 2:33-38,
1964. BibTeX entry |
| [243] | E. Boros. On certain properties of EPr matrices.
An. Univ. Timisoara Ser. Sti. Mat.-Fiz. No., 3:77-84, 1965. BibTeX entry |
| [244] | E. Boros. Das verallgemeinerte Inverse eines linearen Operators in
Vektorräumen mit nicht ausgearteter Hermitescher Metrik über
einem kommutativen Körper. J. Reine Angew. Math., 252:68-78,
1972. BibTeX entry |
| [245] | E. Boros. The generalized inverse of linear operators on spaces with
indefinite metric. An. Univ. Timisoara Ser. Stiint. Mat., 21(1-2):9-44,
1983. BibTeX entry |
| [246] | E. Boros and I. Sturz. On quasi-inverse matrices. An. Univ.
Timisoara Ser. Sti. Mat.-Fiz. No., 1:59-66, 1963. BibTeX entry |
| [247] | N. K. Bose and S. K. Mitra. Generalized inverse of polynomial matrices.
IEEE Trans. Automatic Control, 23(3):491-493, 1978. (see also
[1736]
). BibTeX entry |
| [248] | R. C. Bose. The fundamental theorem of linear estimation (abstract).
Proc. 31st Indian Sci. Congress, pages 2-3, 1944. BibTeX entry |
| [249] | R. Bott and R. J. Duffin. On the algebra of networks. Trans.
Amer. Math. Soc., 74:99-109, 1953. BibTeX entry |
| [250] | R. H. Bouldin. The pseudo-inverse of a product. SIAM J. Appl.
Math., 24:489-495, 1973. BibTeX entry |
| [251] | R. H. Bouldin. The product of operators with closed range. Tôhoku
Math. J. (2), 25:359-363, 1973. BibTeX entry |
| [252] | R. H. Bouldin. Selfadjoint approximants. Indiana Univ. Math.
J., 27(2):299-307, 1978. BibTeX entry |
| [253] | R. H. Bouldin. Generalized inverses and factorizations. In Campbell
[318]
, pages 233-249. BibTeX entry |
| [254] | T. L. Boullion. Contributions to the Theory of Pseudoinverses
. PhD thesis, University of Texas, Austin, 1966. BibTeX entry |
| [255] | T. L. Boullion and P. L. Odell, editors. Proceedings of the Symposium
on Theory and Applications Generalized Inverses of Matrices, Lubbock,
1968. Texas Tech. Press. BibTeX entry |
| [256] | T. L. Boullion and P. L. Odell. A note on the Scroggs-Odell pseudoinverse.
SIAM J. Appl. Math., 17:7-10, 1969. (correction of
[1671]
). BibTeX entry |
| [257] | T. L. Boullion and P. L. Odell. Generalized Inverse Matrices
. John Wiley & Sons, New York, 1971. BibTeX entry |
| [258] | T. L. Boullion and G. D. Poole. A characterization of the general
solution of the matrix equation AX+XB=C
. Indust. Math., 20:91-95, 1970. BibTeX entry |
| [259] | Z. Boulmaarouf, M. Fernandez Miranda, and J-Ph. Labrousse. An algorithmic
approach to orthogonal projections and Moore-Penrose inverses. Numer.
Funct. Anal. Optim., 18(1-2):55-63, 1997. BibTeX entry |
| [260] | E. Bounitzky. Sur la fonction de Green des équations differentielles
linéaires ordinaires. J. Math. Pures Appl., 5(6):65-125,
1909. BibTeX entry |
| [261] | N. Bourbaki. Eléments de Mathématiques. Livre V.
Espaces Vectoriels Topologiques. Hermann & Cie, Paris, 1953. BibTeX entry |
| [262] | N. Bourbaki. Eléments de Mathématiques. Livre II.
Algèbre. Hermann & Cie, Paris, 1958. BibTeX entry |
| [263] | H. J. Bowdler, R. S. Martin, G. Peters, and J. H. Wilkinson. Solutions
of real and complex systems of linear equations. Numer. Math., 8:217-239,
1966. (republished, pp. 93-110 in [2058]
). BibTeX entry |
| [264] | V. J. Bowman and C.-A. Burdet. On the general solution to systems
of mixed-integer linear equations. SIAM J. Appl. Math., 26:120-125,
1974. BibTeX entry |
| [265] | Yu. E. Boyarintsev. General solutions of boundary value problems
for singular systems of ordinary differential equations. Cisl. Metody
Meh. Splosn. Sredy, 8(7):12-21, 1977. BibTeX entry |
| [266] | Yu. E. Boyarintsev. A representation of the Drazin inverse matrix.
In Numerical Methods of Optimization (Applied Mathematics) (Russian)
, pages 176-179. Akad. Nauk SSSR Sibirsk. Otdel. Ènerget. Inst.,
Irkutsk, 1978. BibTeX entry |
| [267] | Yu. E. Boyarintsev. Regulyarnye i Singulyarnye Sistemy Lineinykh
Obyknovennykh Differentsialnykh Uravnenii. ``Nauka'' Sibirsk. Otdel.,
Novosibirsk, 1980. BibTeX entry |
| [268] | Yu. E. Boyarintsev. Solving a pair of matrices. In Approximate
Methods for Solving Operator Equations and their Applications, pages
35-47. Akad. Nauk SSSR Sibirsk. Otdel. Ènerget. Inst., Irkutsk,
1982. BibTeX entry |
| [269] | Yu. E. Boyarintsev. Representation of the solutions of a system of
linear algebraic equations by means of generalized inverse matrices.
In Computational Methods in Linear Algebra (Russian) (Moscow, 1982)
, pages 33-45. Akad. Nauk SSSR Otdel Vychisl. Mat., Moscow, 1983. BibTeX entry |
| [270] | Yu. E. Boyarintsev. The solving pair of matrices and its application.
In Current Problems in Numerical and Applied Mathematics (Novosibirsk,
1981), pages 52-55. ``Nauka'' Sibirsk. Otdel., Novosibirsk, 1983. BibTeX entry |
| [271] | Yu. E. Boyarintsev. Degenerate systems and the index of a variable
matrix. In Differential Equations and Numerical Methods, pages
105-114, 277. ``Nauka'' Sibirsk. Otdel., Novosibirsk, 1986. BibTeX entry |
| [272] | Yu. E. Boyarintsev. Methods of Solving Singular Systems of Ordinary
Differential Equations. John Wiley & Sons Ltd., Chichester, 1992.
(translation of the 1988 Russian original). BibTeX entry |
| [273] | Yu. E. Boyarintsev. A resolving transformation of unknowns in an
implicit system of ordinary differential equations. In Algebrodifferential
Systems and Methods for their Solution (Russian), pages 4-19, 90. VO
``Nauka'', Novosibirsk, 1993. BibTeX entry |
| [274] | Yu. E. Boyarintsev, V. A. Danilov, A. A. Loginov, and V. F. Chistyakov.
Chislennye Metody Resheniya Singulyarnykh Sistem. ``Nauka'' Sibirsk.
Otdel., Novosibirsk, 1989. BibTeX entry |
| [275] | Yu. E. Boyarintsev and V. M. Korsukov. The structure of a general
continuously differentiable solution of a boundary value problem for a
singular system of ordinary differential equations. In Questions in
Applied Mathematics (Russian), pages 73-93. Sibirsk. Ènerget.
Inst., Akad. Nauk SSSR Sibirsk. Otdel., Irkutsk, 1977. BibTeX entry |
| [276] | F. Brackx, R. Delanghe, and J. Van hamme. Generalized inverses of
elliptic systems of differential operators with constant coefficients and
related REDUCE programs for explicit calculations. Rend. Circ. Mat.
Palermo (2) Suppl., (16):21-28, 1987. BibTeX entry |
| [277] | H. W. Braden. R-matrices and generalized inverses. J.
Phys. A, 30(15):L485-L493, 1997. BibTeX entry |
| [278] | H. W. Braden. The equations A TX X
TA=B. SIAM J. Matrix Anal. Appl., 20(2):295-302
(electronic), 1999. BibTeX entry |
| [279] | J. S. Bradley. Generalized Green's matrices for compatible differential
systems. Michigan Math. J., 13:97-108, 1966. BibTeX entry |
| [280] | J. S. Bradley. Adjoint quasi-differential operators of Euler type.
Pacific J. Math., 16:213-237, 1966. BibTeX entry |
| [281] | L. Brand. The solution of linear algebraic equations. Math.
Gaz., 46:203-237, 1962. BibTeX entry |
| [282] | C. Brezinski. Projection methods for linear systems. J. Comput.
Appl. Math., 77(1-2):35-51, 1997. (ROLLS Symposium (Leipzig, 1996)). BibTeX entry |
| [283] | C. Brezinski, M. Morandi Cecchi, and M. Redivo Zaglia. The reverse
bordering method. SIAM J. Matrix Anal. Appl., 15(3):922-937, 1994. BibTeX entry |
| [284] | C. Brezinski and M. Redivo Zaglia. Extrapolation Methods. Theory
and practice, With 1 IBM-PC floppy disk (5.25 inch). North-Holland
Publishing Co., Amsterdam, 1991. BibTeX entry |
| [285] | P. Broadbridge and H. G. Petersen. Use of generalized inverses in
the construction of Hamiltonians for constrained dynamical systems. In
Confronting the Infinite (Adelaide, 1994), pages 307-318.
World Sci. Publishing, River Edge, NJ, 1995. BibTeX entry |
| [286] | C. G. den Broeder Jr. and A. Charnes. Contributions to the theory
of generalized inverses for matrices. Dept. of math., Purdue University,
Lafayette, IN, 1957. (Reprinted as ONR Res. Memo. No. 39, Northwestern
University, Evanston, IL, 1962). BibTeX entry |
| [287] | D. S. Broomhead, R. Jones, G. P. King, and E. R. Pike. Singular system
analysis with application to dynamical systems. In Chaos, Noise and
Fractals (Como, 1986), pages 15-27. Hilger, Bristol, 1987. BibTeX entry |
| [288] | K. G. Brown. On ridge estimation in rank deficient models. Comm.
Statist. A-Theory Methods, 7(2):187-192, 1978. BibTeX entry |
| [289] | R. C. Brown. Generalized Green's functions and generalized inverses
for linear differential systems with Stieltjes boundary conditions.
J. Differential Equations, 16:335-351, 1974. BibTeX entry |
| [290] | R. Bru and N. Thome. Group inverse and group involutory matrices.
Linear and Multilinear Algebra, 45(2-3):207-218, 1998. BibTeX entry |
| [291] | R. A. Brualdi. From the Editor-in-Chief. Comment on: ``The explicit
solutions and solvability of matrix equations'' [Linear Algebra Appl.
311 (2000), no. 1-3, 195-199; MR 2000m:15019] by L. Huang. Linear
Algebra and its Applications, 320(1-3):216, 2000. BibTeX entry |
| [292] | R. A. Brualdi and H. Schneider. Determinantal identities : Gauss,
Schur, Cauchy, Sylvester, Kronecker, Jacobi, Binet, Laplace, Muir and Cayley.
Linear Algebra and its Applications, 52:769-791, 1983. BibTeX entry |
| [293] | J. T. Bruening. A new formula for the Moore-Penrose inverse. In
Current Trends in Matrix Theory (Auburn, Ala., 1986), pages
65-74. North-Holland, New York, 1987. BibTeX entry |
| [294] | R. S. Bucy. Comments on a paper by F. E. Udwadia and R. E. Kalaba:
``A new perspective on constrained motion'' [Proc. Roy. Soc. London Ser.
A 439 (1992), no. 1906, 407-410; MR 94b:70027]. Proc. Roy.
Soc. London Ser. A, 444(1920):253-255, 1994. (see
[989]
). BibTeX entry |
| [295] | Hamza Bulut and S. Aysun Bulut. Spectral decompositions and generalized
inverses in a circularization network flow problem. J. Math. Anal.
Appl., 174:390-402, 1993. BibTeX entry |
| [296] | W. Burmeister. Inversionfreie Verfahren zur Lösung nichtlinearer
Operatorgleichungen. Zeit. angew. Math. Mech., 52:101-110, 1972. BibTeX entry |
| [297] | F. Burns, D. Carlson, E. V. Haynsworth, and T. Markham. Generalized
inverse formulas using the Schur complement. SIAM J. Appl. Math.
, 26:254-259, 1974. BibTeX entry |
| [298] | P. A. Businger and G. H. Golub. Linear least squares by Householder
transformations. Numer. Math., 7:269-276, 1965. (republished,
pp. 111-118 in [2058]
). BibTeX entry |
| [299] | P. A. Businger and G. H. Golub. Algorithm 358: Singular value decomposition
of a complex matrix. Comm. ACM, 12:564-565, 1969. BibTeX entry |
| [300] | C. A. Butler and T. D. Morley. A note on the shorted operator.
SIAM J. Matrix Anal. Appl., 9(2):147-155, 1988. BibTeX entry |
| [301] | C. A. Butler and T. D. Morley. Six generalized Schur complements.
Linear Algebra and its Applications, 106:259-269, 1988. BibTeX entry |
| [302] | Kim Ki-Hang Butler. A Moore-Penrose inverse for Boolean relation
matrices. In Combinatorial Mathematics (Proc. Second Australian Conf.,
Univ. Melbourne, Melbourne, 1973), pages 18-28. Lecture Notes in Math.,
Vol. 403. Springer, Berlin, 1974. BibTeX entry |
| [303] | J. A. Cadzow. A finite algorithm for the minimum l solution
to a system of consistent linear equations. SIAM J. Numer. Anal.
, 10:607-617, 1973. BibTeX entry |
| [304] | G. D. Callon and C. W. Groetsch. The method of weighting and approximation
of restricted pseudosolutions. J. Approx. Theory, 51(1):11-18,
1987. BibTeX entry |
| [305] | S. L. Campbell. The Drazin inverse of an infinite matrix. SIAM
J. Appl. Math., 31(3):492-503, 1976. (see [319]
). BibTeX entry |
| [306] | S. L. Campbell. Differentiation of the Drazin inverse. SIAM
J. Appl. Math., 30(4):703-707, 1976. BibTeX entry |
| [307] | S. L. Campbell. Optimal control of autonomous linear processes with
singular matrices in the quadratic cost functional. SIAM J. Control
Optimization, 14(6):1092-1106, 1976. BibTeX entry |
| [308] | S. L. Campbell. Linear systems of differential equations with singular
coefficients. SIAM J. Math. Anal., 8(6):1057-1066, 1977. BibTeX entry |
| [309] | S. L. Campbell. On continuity of the Moore-Penrose and Drazin generalized
inverses. Linear Algebra and Appl., 18(1):53-57, 1977. BibTeX entry |
| [310] | S. L. Campbell. Singular perturbation of autonomous linear systems.
II. J. Differential Equations, 29(3):362-373, 1978. BibTeX entry |
| [311] | S. L. Campbell. Optimal control of discrete linear processes with
quadratic cost. Internat. J. Systems Sci., 9(8):841-847, 1978. BibTeX entry |
| [312] | S. L. Campbell. Nonregular singular dynamic Leontief systems.
Econometrica, 47(6):1565-1568, 1979. BibTeX entry |
| [313] | S. L. Campbell. Limit behavior of solutions of singular difference
equations. Linear Algebra and its Applications, 23:167-178, 1979. BibTeX entry |
| [314] | S. L. Campbell. Continuity of the Drazin inverse. Linear and
Multilinear Algebra, 8(3):265-268, 1979/80. BibTeX entry |
| [315] | S. L. Campbell. On a singularly perturbed autonomous linear control
problem. IEEE Trans. Automat. Control, 24(1):115-117, 1979. BibTeX entry |
| [316] | S. L. Campbell. Singular Systems of Differential Equations
. Pitman (Advanced Publishing Program), Boston, Mass., 1980. BibTeX entry |
| [317] | S. L. Campbell. On an assumption guaranteeing boundary layer convergence
of singularly perturbed systems. Automatica-J. IFAC, 17(4):645-646,
1981. BibTeX entry |
| [318] | S. L. Campbell, editor. Recent Applications of Generalized Inverses
, Boston, Mass., 1982. Pitman (Advanced Publishing Program). BibTeX entry |
| [319] | S. L. Campbell. The Drazin inverse of an operator.
[318]
, pages 250-260. BibTeX entry |
| [320] | S. L. Campbell. On positive controllers and linear quadratic optimal
control problems. Internat. J. Control, 36(5):885-888, 1982. BibTeX entry |
| [321] | S. L. Campbell. Singular Systems of Differential Equations. II
. Pitman (Advanced Publishing Program), Boston, Mass., 1982. BibTeX entry |
| [322] | S. L. Campbell. Index two linear time-varying singular systems of
differential equations. SIAM J. Algebraic Discrete Methods, 4(2):237-243,
1983. BibTeX entry |
| [323] | S. L. Campbell. Control problem structure and the numerical solution
of linear singular systems. Math. Control Signals Systems, 1(1):73-87,
1988. BibTeX entry |
| [324] | S. L. Campbell. Uniqueness of completions for linear time varying
differential algebraic equations. Linear Algebra and its Applications
, 161:55-67, 1992. BibTeX entry |
| [325] | S. L. Campbell. Least squares completions for nonlinear differential
algebraic equations. Numer. Math., 65(1):77-94, 1993. BibTeX entry |
| [326] | S. L. Campbell and C. D. Meyer, Jr. Continuity properties of the
Drazin pseudoinverse. Linear Algebra and its Applications, 10:77-83,
1975. BibTeX entry |
| [327] | S. L. Campbell and C. D. Meyer, Jr. EP operators and
generalized inverses. Canad. Math. Bull, 18(3):327-333, 1975. BibTeX entry |
| [328] | S. L. Campbell and C. D. Meyer, Jr. Weak Drazin inverses. Linear
Algebra and its Applications, 20(2):167-178, 1978. BibTeX entry |
| [329] | S. L. Campbell and C. D. Meyer, Jr. Generalized Inverses of Linear
Transformations. Pitman (Advanced Publishing Program), Boston, Mass.,
1979. (reprinted by Dover, 1991). BibTeX entry |
| [330] | S. L. Campbell, C. D. Meyer, Jr., and N. J. Rose. Applications of
the Drazin inverse to linear systems of differential equations with singular
constant coefficients. SIAM J. Appl. Math., 31(3):411-425, 1976.
(see [1464]
, [400]
, [763]
, [2057]
). BibTeX entry |
| [331] | S. L. Campbell and G. D. Poole. Convergent regular splittings for
nonnegative matrices. Linear and Multilinear Algebra, 10(1):63-73,
1981. BibTeX entry |
| [332] | S. L. Campbell and G. D. Poole. Computing nonnegative rank factorizations.
Linear Algebra and its Applications, 35:175-182, 1981. BibTeX entry |
| [333] | S. L. Campbell and M. Rakowski. Explicit formulae for completions
of linear time varying singular systems of differential equations.
Circuits Systems Signal Process., 13(2-3):185-199, 1994. BibTeX entry |
| [334] | S. L. Campbell and N. J. Rose. Singular perturbation of autonomous
linear systems. III. Houston J. Math., 4(4):527-539, 1978. BibTeX entry |
| [335] | S. L. Campbell and N. J. Rose. Singular perturbation of autonomous
linear systems. SIAM J. Math. Anal., 10(3):542-551, 1979. BibTeX entry |
| [336] | S. L. Campbell and N. J. Rose. A second order singular linear system
arising in electric power systems analysis. Internat. J. Systems Sci.
, 13(1):101-108, 1982. BibTeX entry |
| [337] | S. L. Campbell and K. D. Yeomans. Behavior of the nonunique terms
in general DAE integrators. Appl. Numer. Math., 28(2-4):209-226,
1998. BibTeX entry |
| [338] | Wei Ping Cao and Ji Pu Ma. Perturbation of A + 0h.
Numer. Math. J. Chinese Univ. (English Ser.), 3(1):96-103, 1994. BibTeX entry |
| [339] | Wei Ping Cao and Ji Pu Ma. The pointwise continuity of the M-P generalized
inverses A + x. Acta Math. Sinica, 40(2):287-295,
1997. BibTeX entry |
| [340] | Wei Ping Cao and Ji Pu Ma. Moore-Penrose generalized inverses of
closed operators. Nanjing Daxue Xuebao Shuxue Bannian Kan, 16(1):75-81,
1999. BibTeX entry |
| [341] | S. R. Caradus. An equational approach to products of relatively regular
operators. Aequationes Math., 15(1):55-62, 1977. BibTeX entry |
| [342] | S. R. Caradus. Generalized Inverses and Operator Theory.
Queen's University, Kingston, Ont., 1978. BibTeX entry |
| [343] | D. Carlson. Matrix decompositions involving the Schur complement.
SIAM J. Appl. Math., 28:577-587, 1975. BibTeX entry |
| [344] | D. Carlson. What are Schur complements, anyway? Linear Algebra
and its Applications, 74:257-275, 1986. BibTeX entry |
| [345] | D. Carlson. Generalized inverse invariance, partial orders, and rank-minimization
problems for matrices. In Current Trends in Matrix Theory (Auburn,
Ala., 1986), pages 81-87. North-Holland, New York, 1987. BibTeX entry |
| [346] | D. Carlson, E. V. Haynsworth, and T. Markham. A generalization of
the Schur complement by means of the Moore-Penrose inverse. SIAM J.
Appl. Math., 26:169-175, 1974. BibTeX entry |
| [347] | R. Caron, H. J. Greenberg, and A. Holder. Analytic centers and repelling
inequalities. Technical Report CCM 142, Center for Computational Mathematics,
University of Colorado at Denver, 1999. (to appear in European Journal
of Operations Research). BibTeX entry |
| [348] | N. Castro González. On the convergence of semiiterative methods
to the Drazin inverse solution of linear equations in Banach spaces.
Collect. Math., 46(3):303-314, 1995. BibTeX entry |
| [349] | N. Castro González and J. J. Koliha. Semi-iterative methods
for the Drazin inverse solution of linear equations in Banach spaces.
Numer. Funct. Anal. Optim., 20(5-6):405-418, 1999. BibTeX entry |
| [350] | N. Castro González and J. J. Koliha. Perturbation of the Drazin
inverse for closed linear operators. Integral Equations Operator Theory
, 36(1):92-106, 2000. BibTeX entry |
| [351] | N. Castro González, J. J. Koliha, and I. Straskraba. Perturbation
of the Drazin inverse. Soochow J. Math., 27(2):201-211, 2001. BibTeX entry |
| [352] | N. Castro González, J. J. Koliha, and Yimin Wei. Perturbation
of the Drazin inverse for matrices with equal eigenprojections at zero.
Linear Algebra and its Applications, 312(1-3):181-189, 2000. BibTeX entry |
| [353] | D. E. Catlin. Estimation, Control, and the Discrete Kalman Filter
. Springer-Verlag, New York, 1989. (see, in particular, pp. 100-113). BibTeX entry |
| [354] | Jian Miao Cen. Fuzzy matrix partial orderings and generalized inverses.
Fuzzy Sets and Systems, 105(3):453-458, 1999. BibTeX entry |
| [355] | B. L. Chalmers, F. T. Metcalf, and B. Shekhtman. On the computation
of minimal projections: millennium report. In Applied Mathematics Reviews,
Vol. 1, pages 119-156. World Sci. Publishing, River Edge, NJ, 2000. BibTeX entry |
| [356] | N. N. Chan. On a downdating formula for regression. J. Statist.
Plann. Inference, 46(3):347-350, 1995. (see
[530]
). BibTeX entry |
| [357] | E. Chang. The generalized inverse and interpolation theory. In
Campbell [318]
, pages 196-219. BibTeX entry |
| [358] | A. Charnes and W. W. Cooper. Structural sensitivity analysis in linear
programming and an exact product form left inverse. Naval Res. Logist.
Quart., 15:517-522, 1968. BibTeX entry |
| [359] | A. Charnes, W. W. Cooper, and G. L. Thompson. Constrained generalized
medians and hypermedians as deterministic equivalents for two-stage linear
programs under uncertainty. Management Sci., 12:83-112, 1965. BibTeX entry |
| [360] | A. Charnes and F. Granot. Existence and representation of Diophantine
and mixed Diophantine solutions to linear equations and inequalities.
Center for cybernetic studies, The University of Texas, Austin, TX, 1973. BibTeX entry |
| [361] | A. Charnes and M. J. L. Kirby. Modular design, generalized inverses
and convex programming. Operations Res., 13:836-847, 1965. BibTeX entry |
| [362] | Guoliang Chen, Musheng Wei, and Yifeng Xue. Perturbation analysis
of the least squares solution in Hilbert spaces. Linear Algebra and
its Applications, 244:69-80, 1996. BibTeX entry |
| [363] | Guoliang Chen and Yimin Wei. Perturbation analysis for the projection
of a point onto an affine set in a Hilbert space. Chinese Ann. Math.
Ser. A, 19(4):405-410, 1998. (translation in Chinese J. Contemp.
Math. 19(1998), 245-252). BibTeX entry |
| [364] | Guoliang Chen and Yifeng Xue. Perturbation analysis for the operator
equation Tx=b in Banach spaces. J. Math. Anal.
Appl., 212(1):107-125, 1997. BibTeX entry |
| [365] | Guoliang Chen and Yifeng Xue. The expression of the generalized inverse
of the perturbed operator under Type I perturbation in Hilbert spaces.
Linear Algebra and its Applications, 285(1-3):1-6, 1998. BibTeX entry |
| [366] | Han Fu Chen. Two kinds of linear estimators in Hilbert spaces, and
their connection. Acta Math. Sinica, 25(6):671-679, 1982. BibTeX entry |
| [367] | X. Chen, M. Z. Nashed, and L. Qi. Convergence of Newton's method
for singular smooth and nonsmooth equations using adaptive outer inverses.
SIAM J. Optim., 7:445-462, 1997. BibTeX entry |
| [368] | Xuzhou Chen and R. E. Hartwig. The hyperpower iteration revisited.
Linear Algebra Appl., 233:207-229, 1996. BibTeX entry |
| [369] | Xuzhou Chen and R. E. Hartwig. The group inverse of a triangular
matrix. Linear Algebra and its Applications, 237/238:97-108, 1996. BibTeX entry |
| [370] | Xuzhou Chen and R. E. Hartwig. On the convergence of power scaled
Cesàro sums. Linear Algebra and its Applications, 267:335-358,
1997. BibTeX entry |
| [371] | Yong-Lin Chen. On the weighted projector and weighted generalized
inverse matrices. Acta Math. Appl. Sinica, 6(3):282-291, 1983. BibTeX entry |
| [372] | Yong-Lin Chen. The generalized Bott-Duffin inverse and its applications.
Linear Algebra and its Applications, 134:71-91, 1990. BibTeX entry |
| [373] | Yong-Lin Chen. A Cramer rule for solution of the general restricted
linear equation. Linear and Multilinear Algebra, 34(2):177-186,
1993. BibTeX entry |
| [374] | Yong-Lin Chen. Representations and Cramer rules for the solution
of a restricted matrix equation. Linear and Multilinear Algebra
, 35(3-4):339-354, 1993. BibTeX entry |
| [375] | Yong-Lin Chen. An explicit representation of the general solution
to a system of constrained linear equations and Cramer's rule. Gaoxiao
Yingyong Shuxue Xuebao, 8(1, Ser. A):61-70, 1993. BibTeX entry |
| [376] | Yong-Lin Chen. Finite algorithms for the (2)-generalized inverse
A (2) T,S. Linear and Multilinear Algebra
, 40(1):61-68, 1995. BibTeX entry |
| [377] | Yong-Lin Chen. Iterative methods for solving restricted linear equations.
Appl. Math. Comput., 86(2-3):171-184, 1997. BibTeX entry |
| [378] | Yong-Lin Chen. Defining equations and explicit expressions for the
generalized inverse A T,S (2). J. Nanjing Norm.
Univ. Nat. Sci. Ed., 23(2):5-8, 2000. BibTeX entry |
| [379] | Yong-Lin Chen and Xin Chen. Representation and approximation of the
outer inverse A (2) T,S of a matrix A.
Linear Algebra and its Applications, 308(1-3):85-107, 2000. BibTeX entry |
| [380] | Yonghong Chen, S. J. Kirkland, and M. Neumann. Group generalized
inverses of M-matrices associated with periodic and nonperiodic
Jacobi matrices. Linear and Multilinear Algebra, 39(4):325-340,
1995. BibTeX entry |
| [381] | Yonghong Chen, S. J. Kirkland, and M. Neumann. Nonnegative alternating
circulants leading to M-matrix group inverses. Linear Algebra
and its Applications, 233:81-97, 1996. BibTeX entry |
| [382] | Yonghong Chen and M. Neumann. M-matrix generalized inverses
of M-matrices. Linear Algebra and its Applications, 256:263-285,
1997. BibTeX entry |
| [383] | Zi Kuan Chen. Finding the synthetic discriminant function for any
sample set by means of the two-step pseudoinverse method. J. Numer.
Methods Comput. Appl., 17(1):8-13, 1996. BibTeX entry |
| [384] | E. W. Cheney. Introduction to Approximation Theory. McGraw-Hill
Book Co., New York, 1966. BibTeX entry |
| [385] | H. Chernoff. Locally optimal designs for estimating parameters.
Ann. Math. Statist., 24:586-602, 1953. BibTeX entry |
| [386] | V. A. Cheverda and V. I. Kostin. r-pseudoinverses for compact
operators in Hilbert spaces: existence and stability. J. Inverse Ill-Posed
Probl., 3(2):131-148, 1995. BibTeX entry |
| [387] | J. S. Chipman. On least squares with insufficient observations.
J. Amer. Statist. Assoc., 54:1078-1111, 1964. (see
[1977]
). BibTeX entry |
| [388] | J. S. Chipman. Specification problems in regression analysis. In
Boullion and Odell [255]
, pages 114-176. BibTeX entry |
| [389] | J. S. Chipman. ``Proofs'' and proofs of the Eckart-Young theorem.
In Stochastic Processes and Functional Analysis (Riverside, CA, 1994)
, pages 71-83. Dekker, New York, 1997. BibTeX entry |
| [390] | J. S. Chipman. Linear restrictions, rank reduction, and biased estimation
in linear regression. Linear Algebra and its Applications, 289(1-3):55-74,
1999. BibTeX entry |
| [391] | J. S. Chipman and M. M. Rao. Projections, generalized inverses and
quadratic forms. J. Math. Anal. Appl., 9:1-11, 1964. BibTeX entry |
| [392] | J. S. Chipman and M. M. Rao. On the treatment of linear restrictions
in regression analysis. Econometrica, 32:198-209, 1964. BibTeX entry |
| [393] | H. Chitwood. Generalized Green's matrices for linear differential
systems. SIAM J. Math. Anal., 4:104-110, 1973. BibTeX entry |
| [394] | Han Hyuk Cho. Regular fuzzy matrices and fuzzy equations. Fuzzy
Sets and Systems, 105(3):445-451, 1999. BibTeX entry |
| [395] | K. K. Choong and J. Y. Kim. A numerical strategy for computing the
stability boundaries for multi-loading systems by using generalized inverse
and continuation method. Engineering Structures, 23:715-724, 2001. BibTeX entry |
| [396] | Shui-Nee Chow and Yun Qiu Shen. Bifurcations via singular value decompositions.
Appl. Math. Comput., 28(3, part I):231-245, 1988. BibTeX entry |
| [397] | Ole Christensen. Frames and pseudo-inverses. J. Math. Anal.
Appl., 195(2):401-414, 1995. BibTeX entry |
| [398] | Ole Christensen. Operators with closed range, pseudo-inverses, and
perturbation of frames for a subspace. Canad. Math. Bull., 42(1):37-45,
1999. BibTeX entry |
| [399] | Ole Christensen. Frames, Riesz bases, and discrete Gabor/wavelet
expansions. Bull. Amer. Math. Soc., 38(3):273-291, 2001. BibTeX entry |
| [400] | M. A. Christodoulou and P. N. Paraskevopoulos. Solvability, controllability,
and observability of singular systems. J. Optim. Theory Appl., 45(1):53-72,
1985. BibTeX entry |
| [401] | Moody T. Chu. On a numerical treatment for the curve-tracing of the
homotopy method. Numer. Math., 42(3):323-329, 1983. BibTeX entry |
| [402] | Moody T. Chu, R. E. Funderlic, and G. H. Golub. On a variational
formulation of the generalized singular value decomposition. SIAM
J. Matrix Anal. Appl., 18(4):1082-1092, 1997. BibTeX entry |
| [403] | Kai Lai Chung. Elementary Probability Theory with Stochastic
Processes. Springer-Verlag, New York, 1974. BibTeX entry |
| [404] | G. Ciecierska. A note on another method of computing the Moore-Penrose
inverse of a matrix. Demonstratio Math., 31(4):879-886, 1998. BibTeX entry |
| [405] | G. Cimmino. Inversione delle corrispondenze funzionali lineari ed
equazioni differenziali. Rivista Mat. Univ. Parma, 1:105-116,
1950. BibTeX entry |
| [406] | G. Cimmino. Cramer's rule without the notion of determinant.
Atti Accad. Sci. Istit. Bologna Cl. Sci. Fis. Rend. (14), 3:115-138
(1987), 1985/86. BibTeX entry |
| [407] | G. Cimmino. An unusual way of solving linear systems. Atti Accad.
Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8), 80(1-2):6-7 (1987),
1986. BibTeX entry |
| [408] | G. Cimmino. On some identities involving spherical means. Atti
Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8), 83:69-72 (1990),
1989. BibTeX entry |
| [409] | J. F. Claerbout. Geophysical Estimation by Example. Stanford
Exploration Project, Stanford University, 2001. (on-line book). BibTeX entry , http://sep.stanford.edu/sep/prof/gee/toc_html/index.html |
| [410] | J. A. Clarkson. Uniformly convex spaces. Trans. Amer. Math.
Soc., 40:396-414, 1936. BibTeX entry |
| [411] | J.-J. Climent, M. Neumann, and A. Sidi. A semi-iterative method for
real spectrum singular linear systems with an arbitrary index. J.
Comput. Appl. Math., 87(1):21-38, 1997. BibTeX entry |
| [412] | J.-J. Climent, N. Thome, and Yimin Wei. A geometrical approach on
generalized inverses by Neumann-type series. Linear Algebra and its
Applications, 332/334:533-540, 2001. BibTeX entry |
| [413] | R. E. Cline. Representations for the generalized inverse of a partitioned
matrix. J. Soc. Indust. Appl. Math., 12:588-600, 1964. BibTeX entry |
| [414] | R. E. Cline. Representations for the generalized inverse of sums
of matrices. J. Soc. Indust. Appl. Math. Ser. B. Numer. Anal., 2:99-114,
1965. BibTeX entry |
| [415] | R. E. Cline. Inverses of rank invariant powers of a matrix.
SIAM J. Appl. Math., 5:182-197, 1968. BibTeX entry |
| [416] | R. E. Cline. Elements of the Theory of Generalized Inverses for
Matrices. (UMAP modules and monographs in undergraduate mathematics and
its applications project). The UMAP Expository Monograph Series).
EDC/UMAP, Newton, Mass., 1979. BibTeX entry |
| [417] | R. E. Cline. Note on an extension of the Moore-Penrose inverse.
Linear Algebra and its Applications, 40:19-23, 1981. BibTeX entry |
| [418] | R. E. Cline and R. E. Funderlic. The rank of a difference of matrices
and associated generalized inverses. Linear Algebra and its Applications
, 24:185-215, 1979. BibTeX entry |
| [419] | R. E. Cline and T. N. E. Greville. An extension of the generalized
inverse of a matrix. SIAM J. Appl. Math., 19:682-688, 1970. BibTeX entry |
| [420] | R. E. Cline and T. N. E. Greville. A Drazin inverse for rectangular
matrices. Linear Algebra and its Applications, 29:53-62, 1980. BibTeX entry |
| [421] | R. E. Cline and R. J. Plemmons. l2-solutions to underdetermined
linear systems. SIAM Rev., 18(1):92-106, 1976. BibTeX entry |
| [422] | R. E. Cline and L. D. Pyle. The generalized inverse in linear programming.
an intersecton projection method and the solution of a class of structured
linear programming problems. SIAM J. Appl. Math., 24:338-351,
1973. BibTeX entry |
| [423] | E. A. Coddington and N. Levinson. Theory of Ordinary Differential
Equations. McGraw-Hill Book Co., 1955. BibTeX entry |
| [424] | L. Collatz. Aufgaben monotoner Art. Arch. Math., 3:366-376,
1952. BibTeX entry |
| [425] | D. Constales. A closed formula for the Moore-Penrose generalized
inverse of a complex matrix of given rank. Acta Math. Hungar.,
80(1-2):83-88, 1998. BibTeX entry |
| [426] | G. Corach, A. Maestripieri, and D. Stojanoff. Generalized orthogonal
projections and shorted operators. In Margarita mathematica, pages
607-625. Univ. La Rioja, Logroño, 2001. BibTeX entry |
| [427] | G. Corach, A. Maestripieri, and D. Stojanoff. Oblique projections
and Schur complements. Acta Sci. Math. (Szeged), 67(1-2):337-356,
2001. BibTeX entry |
| [428] | G. Corach, A. Maestripieri, and D. Stojanoff. Generalized Schur complements
and oblique projections. Linear Algebra and its Applications, 341:259-272,
2002. BibTeX entry |
| [429] | G. Corach, H. Porta, and L. Recht. Differential geometry of spaces
of relatively regular operators. Integral Equations Operator Theory
, 13(6):771-794, 1990. BibTeX entry |
| [430] | C. Corradi. A note on the solution of separable nonlinear least-squares
problems with separable nonlinear equality constraints. SIAM J. Numer.
Anal., 18(6):1134-1138, 1981. BibTeX entry |
| [431] | C. Corradi. Computing methods for restricted estimation in linear
models. Statistica (Bologna), 42(1):55-68, 1982. (see
[645]
). BibTeX entry |
| [432] | R. W. Cottle. Manifestations of the Schur complement. Linear
Algebra and Appl., 8:189-211, 1974. BibTeX entry |
| [433] | R. Courant. Differential and Integral Calculus. Interscience
Publishers, New York, 1936. (translated by E.J. McShane). BibTeX entry |
| [434] | R. Courant and D. Hilbert. Methods of Mathematical Physics. Vol.
I. Interscience Publishers, New York, 1953. (First published in German
1924). BibTeX entry |
| [435] | D. E. Crabtree and E. V. Haynsworth. An identity for the Schur complement
of a matrix. Proc. Amer. Math. Soc., 22:364-366, 1969. BibTeX entry |
| [436] | D. F. Cudia. Rotundity. In Convexity, Proc. Sympos. Pure Math.
Vol. VII (V. Klee, Editor), pages 73-97. Amer. Math. Soc., Providence,
R.I., 1963. BibTeX entry |
| [437] | C. G. Cullen and K. J. Gale. A functional definition of the determinant.
Amer. Math. Monthly, 72:403-406, 1965. BibTeX entry |
| [438] | B. Cvetkov. A new method of computation in the theory of least squares.
Austral. J. Appl. Sci., 6:274-280, 1955. BibTeX entry |
| [439] | Hua Dai. An algorithm for symmetric generalized inverse eigenvalue
problems. Linear Algebra and its Applications, 296(1-3):79-98, 1999. BibTeX entry |
| [440] | J. F. Dalphin and V. Lovass-Nagy. Best least squares solutions to
finite difference equations using the generalized inverse and tensor product
methods. Journal of the ACM, 20(2):279-289, 1973. BibTeX entry |
| [441] | J. Dauxois and G. M. Nkiet. Canonical analysis of two Euclidean subspaces
and its applications. Linear Algebra and its Applications, 264:355-388,
1997. BibTeX entry |
| [442] | D. F. Davidenko. On a new method of numerical solution of systems
of nonlinear equations. Doklady Akad. Nauk SSSR (N.S.), 88:601-602,
1953. BibTeX entry |
| [443] | D. F. Davidenko. The method of variation of parameters as applied
to the computation of eigenvalues and eigenvectors of matrices. Soviet
Math. Dokl., 1:364-367, 1960. BibTeX entry |
| [444] | D. F. Davidenko. The evaluation of determinants by the method of
variation of parameters. Soviet Math. Dokl., 1:316-319, 1960. BibTeX entry |
| [445] | D. F. Davidenko. Inversion of matrices by the method of variation
of parameters. Soviet Math. Dokl., 1:279-282, 1960. BibTeX entry |
| [446] | D. F. Davidenko. Pseudo-inversion and construction of generalized
solutions of linear equations that arise in calculations for nuclear reactors.
In Computational Processes and Systems, No. 6 (Russian), pages
98-109. ``Nauka'', Moscow, 1988. BibTeX entry |
| [447] | C. Davis. Separation of two linear subspaces. Acta Sci. Math.
Szeged, 19:172-187, 1958. BibTeX entry |
| [448] | C. Davis. Completing a matrix so as to minimize the rank. In
Topics in Operator Theory and Interpolation, pages 87-95. Birkhäuser,
Basel, 1988. BibTeX entry |
| [449] | C. Davis and W. M. Kahan. Some new bounds on perturbation of subspaces.
Bull. Amer. Math. Soc., 75:863-868, 1969. BibTeX entry |
| [450] | C. Davis and W. M. Kahan. The rotation of eigenvectors by a perturbation.
III. SIAM J. Numer. Anal., 7:1-46, 1970. BibTeX entry |
| [451] | D. L. Davis and D. W. Robinson. Generalized inverses of morphisms.
Linear Algebra and its Applications, 5:329-338, 1972. BibTeX entry |
| [452] | P. Dean and J. Porrill. Pseudo-inverse control in biological systems:
a learning mechanism for fixation stability. Neural Networks,
11:1205-1218, 1998. BibTeX entry |
| [453] | S. R. Deans. The Radon Transform and some of its Applications
(Revised reprint of the 1983 original). Robert E. Krieger Publishing
Co. Inc., Malabar, FL, 1993. BibTeX entry |
| [454] | H. P. Decell, Jr. An alternate form of the generalized inverse of
an arbitrary complex matrix. SIAM Rev., 7:356-358, 1965. (see
[2123]
). BibTeX entry |
| [455] | H. P. Decell, Jr. An application of the Cayley-Hamilton theorem to
generalized matrix inversion. SIAM Rev., 7:526-528, 1965. (extended
in [1928]
). BibTeX entry |
| [456] | H. P. Decell, Jr. On the derivative of the generalized inverse of
a matrix. Linear and Multilinear Algebra, 1:357-359, 1973/74. BibTeX entry |
| [457] | H. P. Decell, Jr. and P. L. Odell. On the fixed point probability
vector of regular or ergodic transition matrices. J. Amer. Statist.
Assoc., 62:600-602, 1967. BibTeX entry |
| [458] | H. P. Decell, Jr. and C. L. Wiginton. A characterization of the maximal
subgroups of the semigroup of n× n complex matrices.
Czechoslovak Math. J., 18 (93):675-677, 1968. BibTeX entry |
| [459] | L. S. Dederick. On the character of a transformation in the neighborhood
of a point where its Jacobian vanishes. Trans. Amer. Math. Soc.
, 14:143-148, 1913. BibTeX entry |
| [460] | J. P. Dedieu and M. Shub. Newton's method for overdetermined systems
of equations. Math. of Comput., 69:1099-1115, 2000. BibTeX entry |
| [461] | L. De Lathauwer, B. De Moor, and J. Vanderwalle. A multilinear singular
value decomposition. SIAM J. Matrix Anal. Appl., 21(4):1253-1278
(electronic), 2000. BibTeX entry |
| [462] | L. De Lathauwer, B. De Moor, and J. Vanderwalle. On the best rank-1
and rank-(R 1,R 2,...,RN) approximation of
higher-order tensors. SIAM J. Matrix Anal. Appl., 21(4):1324-1342
(electronic), 2000. BibTeX entry |
| [463] | F. -J. Delvos. Splines and pseudo-inverses. RAIRO Anal. Numér.
, 12(4):313-324, v, 1978. BibTeX entry |
| [464] | F. -J. Delvos and W. Schempp. Convergence of approximate splines
via pseudo-inverses. RAIRO Modél. Math. Anal. Numér.
, 21(2):261-267, 1987. BibTeX entry |
| [465] | R. de Meersman. Geometric meaning of the method of Golub and Kahan
for the calculation of the singular values of a matrix. Bull. Soc.
Math. Belg., 22:146-154, 1970. BibTeX entry |
| [466] | R. De Meersman. Algorithms for pseudo-inverses of linear mappings.
A unified approach. Bull. Soc. Math. Belg., 23:283-294, 1971. BibTeX entry |
| [467] | R. De Meersman and P. Siau. On updating formulas for least squares
solutions and pseudo-inverses. J. Comput. Appl. Math., 3(4):293-297,
1977. BibTeX entry |
| [468] | B. De Moor. Structured total least squares and l2
approximation problems. Linear Algebra and its Applications, 188/189:163-205,
1993. BibTeX entry |
| [469] | J. B. Dennis. Mathematical Programming and Electrical Networks
. MIT Press, Cambridge, Mass., 1959. BibTeX entry |
| [470] | B. A. Dent and A. Newhouse. Polynomials orthogonal over discrete
domains. SIAM Rev., 1:55-59, 1959. BibTeX entry |
| [471] | A. R. De Pierro and Musheng Wei. Reverse order law for reflexive
generalized inverses of products of matrices. Linear Algebra and its
Applications, 277:299-311, 1998. BibTeX entry |
| [472] | A. R. De Pierro and Musheng Wei. Some new properties of the equality
constrained and weighted least squares problem. Linear Algebra and
its Applications, 320(1-3):145-165, 2000. BibTeX entry |
| [473] | C. A. Desoer and B. H. Whalen. A note on pseudoinverses. J.
Soc. Indust. Appl. Math., 11:442-447, 1963. BibTeX entry |
| [474] | M. Desplas. Matrice pseudo-inverse de Moore-Penrose et variables
duales généralisées en programmation mathématique.
RAIRO Rech. Opér., 26(4):313-360, 1992. BibTeX entry |
| [475] | P. Deuflhard. A modified Newton method for the solution of ill-conditioned
systems of nonlinear equations with application to multiple shooting.
Numer. Math., 22:289-315, 1974. BibTeX entry |
| [476] | P. Deuflhard and G. Heindl. Affine invariant convergence theorems
for Newton's method and extensions to related methods. SIAM J. Numer.
Anal., 16:1-10, 1979. BibTeX entry |
| [477] | P. Deuflhard and W. Sautter. On rank-deficient pseudoinverses.
Linear Algebra and its Applications, 29:91-111, 1980. BibTeX entry |
| [478] | E. Deutsch. Semi-inverses, reflexive semi-inverses, and pseudo-inverses
of an arbitrary linear transformation. Linear Algebra and its Applications
, 4:313-322, 1971. BibTeX entry |
| [479] | E. Deutsch and M. Neumann. Derivatives of the Perron root at an essentially
nonnegative matrix and the group inverse of an M-matrix. J.
Math. Anal. Appl., 102(1):1-29, 1984. BibTeX entry |
| [480] | F. Deutsch. The angle between subspaces of a Hilbert space. In
Approximation Theory, Wavelets and Applications (Maratea, 1994)
, pages 107-130. Kluwer Acad. Publ., Dordrecht, 1995. BibTeX entry |
| [481] | F. Deutsch. Best Approximation in Inner Product Spaces.
Springer-Verlag, New York, 2001. BibTeX entry |
| [482] | O. Y. De Vel and E. V. Krishnamurthy. An iterative pipelined array
architecture for the generalized matrix inversion. Information Processing
Letters, 26(5):263-267, 1988. BibTeX entry |
| [483] | M. E. Díaz Lozano. The class of {1,2,4}-inverses as the solution
of a linear problem. Bol. Soc. Mat. Mexicana (3), 4(2):223-228,
1998. BibTeX entry |
| [484] | V. D. Didenko and B. Silbermann. Extension of C *-algebras
and Moore-Penrose stability of sequences of additive operators. Linear
Algebra and its Applications, 275/276:121-140, 1998. BibTeX entry |
| [485] | F. Diele, L. Lopez, and R. Peluso. The Cayley transform in the numerical
solution of unitary differential systems. Adv. Comput. Math.,
8(4):317-334, 1998. BibTeX entry |
| [486] | I. I. Dikin. On the speed of an iterative process. Upravlyaemye
Sistemi, 12:54-60, 1974. (see [1899]
). BibTeX entry |
| [487] | L. L. Dines. Projective transformations in function space. Trans.
Amer. Math. Soc., 20:45-65, 1919. (see p. 403 and
[898]
). BibTeX entry |
| [488] | Jiu Ding. Perturbation results for projecting a point onto a linear
manifold. SIAM J. Matrix Anal. Appl., 19(3):696-700 (electronic),
1998. BibTeX entry |
| [489] | Jiu Ding. Perturbation of systems of linear algebraic equations.
Linear and Multilinear Algebra, 47(2):119-127, 2000. BibTeX entry |
| [490] | Jiu Ding. Lower and upper bounds in the perturbation of general linear
algebraic equations. Appl. Math. Lett., 14(1):49-52, 2001. BibTeX entry |
| [491] | Jiu Ding and Liang Jiao Huang. On the perturbation of the least squares
solutions in Hilbert spaces. Linear Algebra and its Applications
, 212/213:487-500, 1994. BibTeX entry |
| [492] | Jiu Ding and Liang Jiao Huang. Perturbation of generalized inverses
of linear operators in Hilbert spaces. J. Math. Anal. Appl., 198(2):506-515,
1996. BibTeX entry |
| [493] | Jiu Ding and Liang Jiao Huang. On the continuity of generalized inverses
of linear operators in Hilbert spaces. Linear Algebra and its Applications
, 262:229-242, 1997. BibTeX entry |
| [494] | D. S. Djordjevic and P. S. Stanimirovic. Universal iterative methods
for computing generalized inverses. Acta Math. Hungar., 79(3):253-268,
1998. BibTeX entry |
| [495] | D. S. Djordjevic and P. S. Stanimirovic. Applications of the Groetsch
theorem. Indian J. Pure Appl. Math., 31(3):277-286, 2000. BibTeX entry |
| [496] | M. Dobovisek. On minimal solutions of the matrix equation A
X-YB=0. Linear Algebra Appl., 325(1-3):81-99,
2001. BibTeX entry |
| [497] | Dragomir Z. Dokovic. On the generalized inverse for matrices.
Glasnik Mat.-Fiz. Astronom. Ser. II Drustvo Mat. Fiz. Hrvatske, 20:51-55,
1965. BibTeX entry |
| [498] | J. Dommanget. L'inverse d'un cracovien rectangulaire: Son emploi
dans la résolution des systèmes d'équations linéaires.
Publ. Sci. Tech. Ministère de l'Air (Paris) Notes Tech. No.
, 128:11-41, 1963. BibTeX entry |
| [499] | J. Douglas, Jr. and C. M. Pearcy. On convergence of alternating direction
procedures in the presence of singular operators. Numer. Math.
, 5:175-184, 1963. BibTeX entry |
| [500] | A. Doust and V. E. Price. The latent roots and vectors of a singular
matrix. Comput. J., 7:222-227, 1964. BibTeX entry |
| [501] | A. Dragomir. On the generalized inverse of a matrix. An. Univ.
Timisoara Ser. Sti. Mat.-Fiz. No., 3:123-128, 1965. BibTeX entry |
| [502] | A. Dragomir and P. Dragomir. Formulas of the Bjerhammar type for
the generalized inverse of an arbitrary matrix. In Proceedings of
the Conference on Algebra (Romanian) (Timisoara, 1986), pages 33-36,
Timisoara, 1987. Univ. Timi soara. BibTeX entry |
| [503] | A. Dragomir and M. Fildan. L'inverse généralisé
d'un opérateur linéaire. An. Univ. Timisoara Ser. Sti.
Mat., 7:55-65, 1969. BibTeX entry |
| [504] | P. Dragomir. On the Greville-Moore formula for calculating the generalized
inverse matrix. An. Univ. Timisoara Ser. Sti. Mat.-Fiz. No., 1:115-119,
1963. BibTeX entry |
| [505] | P. Dragomir. The generalized inverse of a bilinear form. An.
Univ. Timisoara Ser. Sti. Mat.-Fiz. No., 2:71-76, 1964. BibTeX entry |
| [506] | M. P. Drazin. Pseudo inverses in associative rings and semigroups.
Amer. Math. Monthly, 65:506-514, 1958. BibTeX entry |
| [507] | M. P. Drazin. Natural structures on semigroups with involution.
Bull. Amer. Math. Soc., 84(1):139-141, 1978. BibTeX entry |
| [508] | M. P. Drazin. Differentiation of generalized inverses. In Campbell
[318]
, pages 138-144. BibTeX entry |
| [509] | M. P. Drazin. A partial order in completely regular semigroups.
J. Algebra, 98:362-374, 1986. BibTeX entry |
| [510] | M. P. Drazin. Extremal definitions of generalized inverses.
Linear Algebra and its Applications, 165:185-196, 1992. BibTeX entry |
| [511] | Pierre Druilhet. Optimality of neighbour balanced designs. J.
Statist. Plann. Inference, 81(1):142-152, 1999. BibTeX entry |
| [512] | V. Drygalla. Zur Darstellung und Berechnung von verallgemeinerten
inversen Matrizen. Mathematics dissertation, Martin-Luther Universität,
Halle-Wirtenberg, 1980. BibTeX entry |
| [513] | V. Drygalla. Refinement of pseudosolutions of a system of linear
equations. Zh. Vychisl. Mat. i Mat. Fiz., 22(5):1027-1032, 1275,
1982. (English translation: U.S.S.R. Comput. Math. and Math. Phys
22(1982), 1-7). BibTeX entry |
| [514] | V. Drygalla. Zur Berechnung von Lösungen konsistenter linearer
Gleichungssysteme mit singulärer Koeffizientenmatrix. Computing
, 36(1-2):163-168, 1986. BibTeX entry |
| [515] | H. Drygas. On a generalization of the Farkas theorem. Unternehmensforschung
, 13:283-290, 1969. BibTeX entry |
| [516] | H. Drygas. The Coordinate-Free Approach to Gauss-Markov Estimation
. Springer-Verlag, Berlin, 1970. BibTeX entry |
| [517] | H. Drygas. Consistency of the least squares and Gauss-Markov estimators
in regression models. Z. Wahrscheinlichkeitstheorie u. verw. Gebiete
, 17:309-326, 1971. BibTeX entry |
| [518] | H. Drygas. Estimation and prediction for linear models in general
spaces (Vorträge auf der Ersten Sommerschule über Probleme der
Modellwahl und Parameterschätzung in der Regressions-Analyse, Zinnowitz,
1974). Math. Operationsforsch. Statist., 6(2):301-324, 1975. BibTeX entry |
| [519] | H. Drygas. Gauss-Markov estimation for multivariate linear models
with missing observations. Ann. Statist., 4(4):779-787, 1976. BibTeX entry |
| [520] | H. Drygas. On the unified theory of least squares. Probab. Math.
Statist., 5(2):177-186, 1985. BibTeX entry |
| [521] | H. Drygas and J. Srzednicka. A new result on Hsu's model of regression
analysis. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys.
, 24(12):1133-1136, 1976. BibTeX entry |
| [522] | R. J. Duffin. Network models. In Wilf and Harary
[2054]
, pages 65-91. BibTeX entry |
| [523] | R. J. Duffin and T. D. Morley. Inequalities induced by network connections.
II. Hybrid connections. J. Math. Anal. Appl., 67(1):215-231, 1979. BibTeX entry |
| [524] | R. J. Duffin and T. D. Morley. Inequalities induced by network connections.
In Campbell [318]
, pages 27-49. BibTeX entry |
| [525] | R. J. Duffin and A. C. Schaeffer. A class of nonharmonic Fourier
series. Trans. Amer. Math. Soc., 72:341-366, 1952. BibTeX entry |
| [526] | R. J. Duffin and G. E. Trapp. Hybrid addition of matrices-network
theory concept. Applicable Anal., 2:241-254, 1972/73. BibTeX entry |
| [527] | J. W. Duke. A note on EP linear transformations. Linear Algebra
and its Applications, 3:379-382, 1970. BibTeX entry |
| [528] | D. B. Duncan and S. D. Horn. Linear dynamic recursive estimation
from the viewpoint of regression analysis. J. Amer. Statist. Assoc.
, 67:815-821, 1972. (connection between Kalman filter and least-squares
regression)). BibTeX entry |
| [529] | N. Dunford and J. T. Schwartz. Linear Operators. Part I.
Interscience, New York, 1957. BibTeX entry |
| [530] | T. T. Dunne and M. Stone. Downdating the Moore-Penrose generalized
inverse for cross-validation of centred least squares prediction.
J. Roy. Statist. Soc. Ser. B, 55(2):369-375, 1993. BibTeX entry |
| [531] | Arthur M. DuPré and Seymour Kass. Distance and parallelism
between flats in n. Linear Algebra and its Applications
, 171:99-107, 1992. BibTeX entry |
| [532] | C. S. Duris. Optimal quadrature formulas using generalized inverses.
I. General theory and minimum variance formulas. Math. Comp.,
25:495-504, 1971. BibTeX entry |
| [533] | C. S. Duris and V. P. Sreedharan. Chebyshev and l1-solutions
of linear equations using least squares solutions. SIAM J. Numer.
Anal., 5:491-505, 1968. BibTeX entry |
| [534] | P. S. Dwyer. Some applications of matrix derivatives in multivariate
analysis. J. Amer. Statist. Assoc, 62:607-625, 1967. BibTeX entry |
| [535] | P. S. Dwyer and M. S. Macphail. Symbolic matrix derivatives.
Ann. Math. Statistics, 19:517-534, 1948. BibTeX entry |
| [536] | S. Dzumaev and È. Muhamadiev. Some properties of a pseudoinverse
operator. Dokl. Akad. Nauk Tadzhik. SSR, 23(1):3-5, 1980. BibTeX entry |
| [537] | N. Eagambaram. Generalized inverses with nonnegative principal minors.
Linear Algebra and its Applications, 111:293-312, 1988. BibTeX entry |
| [538] | N. Eagambaram. (i,j,...,k)-inverses via bordered
matrices. Sankhya Ser. A, 53(3):298-308, 1991. BibTeX entry |
| [539] | M. L. Eaton. Multivariate Statistics. John Wiley & Sons
Inc., New York, 1983. A vector space approach. BibTeX entry |
| [540] | C. Eckart and G. Young. The approximation of one matrix by another
of lower rank. Psychometrika, 1:211-218, 1936. BibTeX entry |
| [541] | C. Eckart and G. Young. A principal axis transformation for non-Hermitian
matrices. Bull. Amer. Math. Soc., 45:118-121, 1939. BibTeX entry |
| [542] | E. Egerváry. On a property of the projector matrices and its
application to the canonical representation of matrix functions. Acta
Sci. Math. Szeged, 15:1-6, 1953. BibTeX entry |
| [543] | M. Eiermann, I. Marek, and W. Niethammer. On the solution of singular
linear systems of algebraic equations by semi-iterative methods. Numer.
Math., 53(3):265-283, 1988. BibTeX entry |
| [544] | S. C. Eisenstat and I. C. F. Ipsen. Relative perturbation techniques
for singular value problems. SIAM J. Numer. Anal., 32(6):1972-1988,
1995. BibTeX entry |
| [545] | S. C. Eisenstat and I. C. F. Ipsen. Relative perturbation results
for eigenvalues and eigenvectors of diagonalisable matrices. BIT
, 38(3):502-509, 1998. BibTeX entry |
| [546] | A. Eisinberg, P. Pugliese, and N. Salerno. Vandermonde matrices on
integer nodes: the rectangular case. Numer. Math., 87(4):663-674,
2001. BibTeX entry |
| [547] | E. Eitelberg and H. Hanselmann. Comments on: ``On system realization
by matrix generalized inverses'' (Internat. J. Control 26 (1977),
no. 5, 745-751) by V. Lovass-Nagy, R. J. Miller and D. L. Powers.
Internat. J. Control, 27(4):651-652, 1978. (see
[1195]
). BibTeX entry |
| [548] | L. Eldén. Perturbation theory for the least squares problem
with linear equality constraints. SIAM J. Numer. Anal., 17:338-350,
1980. BibTeX entry |
| [549] | Eldén. L. A weighted pseudoinverse, generalized singular values,
and constrained least squares problems. BIT, 22:487-502, 1983. BibTeX entry |
| [550] | G. Elfving. Optimum allocation in linear regression theory.
Ann. Math. Statistics, 23:255-262, 1952. BibTeX entry |
| [551] | T. Elfving. A stationary iterative pseudoinverse algorithm.
BIT, 38(2):275-282, 1998. BibTeX entry |
| [552] | L. El Ghaoui and H. Lebret. Robust solutions to least-squares problems
with uncertain data. SIAM J. Matrix Anal. Appl., 18(4):1035-1064,
1997. BibTeX entry |
| [553] | W. W. Elliott. Generalized Green's functions for compatible differential
systems. Amer. J. Math., 50:243-258, 1928. BibTeX entry |
| [554] | W. W. Elliott. Green's functions for differential systems containing
a parameter. Amer. J. Math., 51:397-416, 1929. BibTeX entry |
| [555] | L. Elsner and Kh. D. Ikramov. Normal matrices: an update. Linear
Algebra and its Applications, 285(1-3):291-303, 1998. (see
[735]
). BibTeX entry |
| [556] | C. Elster. Recovering wavefronts from difference measurements in
lateral shearing interferometry. J. Comput. Appl. Math., 110(1):177-180,
1999. BibTeX entry |
| [557] | H. W. Engl and C. W. Groetsch. A higher order approximation technique
for restricted linear least-squares problems. Bull. Austral. Math.
Soc., 37(1):121-130, 1988. BibTeX entry |
| [558] | H. W. Engl, M. Hanke, and A. Neubauer. Regularization of Inverse
Problems. Kluwer Academic Publishers Group, Dordrecht, 1996. BibTeX entry |
| [559] | H. W. Engl and R. Kress. A singular perturbation problem for linear
operators with an application to electrostatic and magnetostatic boundary
and transmission problems. Math. Methods Appl. Sci., 3(2):249-274,
1981. BibTeX entry |
| [560] | H. W. Engl and M. Z. Nashed. New extremal characterizations of generalized
inverses of linear operators. J. Math. Anal. Appl., 82(2):566-586,
1981. BibTeX entry |
| [561] | H. W. Engl and A. Neubauer. On projection methods for solving linear
ill-posed problems. In Model Optimization in Exploration Geophysics
(Berlin, 1986), pages 73-92. Vieweg, Braunschweig, 1987. BibTeX entry |
| [562] | M. J. Englefield. The commuting inverses of a square matrix.
Proc. Cambridge Philos. Soc., 62:667-671, 1966. BibTeX entry |
| [563] | D. Enskog. Über die Auflösung einer singularel Integralgleichung.
Acta Math. Uppsala, 54:177-184, 1930. BibTeX entry |
| [564] | P. J. Erdelsky. Projections in a Normed Linear Space and a Generalization
of the Pseudo-Inverse. Doctoral dissertation in mathematics, California
Inst. Tech., Pasadena, CA, 1969. BibTeX entry |
| [565] | I. Erdélyi. On partial isometries in finite dimensional Euclidean
spaces. SIAM J. Appl. Math., 14:453-467, 1966. BibTeX entry |
| [566] | I. Erdélyi. On the ``reversed order law'' related to the generalized
inverse of matrix products. J. Assoc. Comput. Mach., 13:439-443,
1966. BibTeX entry |
| [567] | I. Erdélyi. The quasi-commuting inverse for a square matrix.
Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. Ser. VIII
, 42:626-633, 1967. BibTeX entry |
| [568] | I. Erdélyi. On the matrix equation Ax=lambda
Bx. J. Math. Anal. Appl., 17:119-132, 1967. BibTeX entry |
| [569] | I. Erdélyi. Partial isometries closed under multiplication
on Hilbert spaces. J. Math. Anal. Appl., 22:546-551, 1968. BibTeX entry |
| [570] | I. Erdélyi. Normal partial isometries closed under multiplication
on unitary spaces. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat.
Natur. Ser. VIII, 43:186-190, 1968. BibTeX entry |
| [571] | I. Erdélyi. Partial isometries defined by a spectral property
on unitary spaces. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat.
Natur. Ser. VIII, 44:741-747, 1968. BibTeX entry |
| [572] | I. Erdélyi. Partial isometries and generalized inverses.
In Boullion and Odell [255]
, pages 203-217. BibTeX entry |
| [573] | I. Erdélyi. A generalized inverse for arbitrary operators
between hilbert spaces. Proceedings of the Cambridge Philosophical Society
, 71:43-50, 1972. BibTeX entry |
| [574] | I. Erdélyi. Spectral decompositions for generalized inversions.
In Campbell [318]
, pages 261-274. BibTeX entry |
| [575] | I. Erdélyi and A. Ben-Israel. Extremal solutions of linear
equations and generalized inversion between Hilbert spaces. J. Math.
Anal. Appl., 39:298-313, 1972. BibTeX entry |
| [576] | I. Erdélyi and F. R. Miller. Decomposition theorems for partial
isometries. J. Math. Anal. Appl., 30:665-679, 1970. BibTeX entry |
| [577] | V. I. Erokhin. A generalization of the Sherman-Morrison identity
to the case of a rank-one modification of a pseudo-inverse matrix of full
rank. Zh. Vychisl. Mat. Mat. Fiz., 39(8):1280-1282, 1999. BibTeX entry |
| [578] | C. A. Eschenbach, F. J. Hall, and Zhongshan Li. Sign pattern matrices
and generalized inverses. Linear Algebra and its Applications, 211:53-66,
1994. BibTeX entry |
| [579] | D. J. Evans, Wenyu Sun, R. J. B. de Sampaio, and J. Y. Yuan. The
restricted generalized inverses corresponding to constrained quadratic
system. Int. J. Comput. Math., 62(3-4):285-296, 1996. BibTeX entry |
| [580] | Ky Fan and A. J. Hoffman. Some metric inequalities in the space of
matrices. Proc. Amer. Math. Soc., 6:111-116, 1955. BibTeX entry |
| [581] | L. Fantappiè. Le calcul des matrices. C. R. Acad. Sci.
Paris, 186:619-621, 1928. (see [1598]
). BibTeX entry |
| [582] | R. W. Farebrother. Further results on the mean square error of ridge
regression. J. Roy. Statist. Soc. Ser. B, 38(3):248-250, 1976. BibTeX entry |
| [583] | R. W. Farebrother. An historical note on recursive residuals.
J. Roy. Statist. Soc. Ser. B, 40(3):373-375, 1978. BibTeX entry |
| [584] | R. W. Farebrother. Relations among set estimators: A bibliographical
note. Technometrics, 27:85-86, 1985. BibTeX entry |
| [585] | R. W. Farebrother. A class of statistical estimators related to principal
components. Linear Algebra and its Applications, 289(1-3):121-126,
1999. BibTeX entry |
| [586] | R. Featherstone and O. Khatib. Load independence of the dynamically
consistent inverse of the jacobian matrix. source. International Journal
of Robotics Research, 16:168-170, 1997. BibTeX entry |
| [587] | H. Federer. Geometric Measure Theory. Springer-Verlag, New
York, 1969. BibTeX entry |
| [588] | C. A. Felippa, K. C. Park, and M. R. Justino Filho. The construction
of free-free flexibility matrices as generalized stiffness inverses.
Computers & Structures, 68:411-418, 1998. BibTeX entry |
| [589] | W. Feller. An Introduction to Probability Theory and Applications,
Volume 1. J. Wiley, New York, 1950. BibTeX entry |
| [590] | I. S. Fenyo. Eine Darstellung der verallgemeinerten Inversen eines
linearen Operators. Ber. Math.-Statist. Sekt. Forsch. Graz, (117):i+15,
1979. BibTeX entry |
| [591] | I. S. Fenyo. A representation of the generalized inverse in Hilbert
spaces. Rend. Sem. Mat. Fis. Milano, 50:23-29 (1982), 1980. BibTeX entry |
| [592] | I. S. Fenyo. An extension of a theorem of Tikhonov. Stochastica
, 8(3):219-228, 1984. BibTeX entry |
| [593] | I. S. Fenyo and E. Paparoni. On an approximation of generalized inverses.
Publ. Math. Debrecen, 33(3-4):239-247, 1986. BibTeX entry |
| [594] | M. Ferrante and P. Vidoni. A Gaussian-generalized inverse Gaussian
finite-dimensional filter. Stochastic Process. Appl., 84(1):165-176,
1999. BibTeX entry |
| [595] | M. Fiedler. Moore-Penrose involutions in the classes of Laplacians
and simplices. Linear and Multilinear Algebra, 39(1-2):171-178,
1995. BibTeX entry |
| [596] | M. Fiedler and T. L. Markham. Some connections between the Drazin
inverse, P-matrices, and the closure of inverse M-matrices.
Linear Algebra and its Applications, 132:163-172, 1990. BibTeX entry |
| [597] | M. Fiedler and T. L. Markham. A characterization of the Moore-Penrose
inverse. Linear Algebra and its Applications, 179:129-133, 1993. BibTeX entry |
| [598] | J. A. Fill and D. E. Fishkind. The Moore-Penrose generalized inverse
for sums of matrices. SIAM J. Matrix Anal. Appl., 21(2):629-635
(electronic), 1999. BibTeX entry |
| [599] | P. A. Filmore and J. P. Williams. On operator ranges. Advances
in Math., 7:254-281, 1971. BibTeX entry |
| [600] | M. Finzel. Linear approximation in l n. J. Approx.
Theory, 76(3):326-350, 1994. BibTeX entry |
| [601] | M. Finzel. Plücker-Grassmann coordinates and elementary vectors.
In Approximation Theory VIII, Vol. 1 (College Station, TX, 1995)
, pages 207-214. World Sci. Publishing, River Edge, NJ, 1995. BibTeX entry |
| [602] | M. Finzel. Metric projection and stratification of the Grassmannian.
Linear Algebra and its Applications, 308(1-3):109-119, 2000. BibTeX entry |
| [603] | A. G. Fisher. On construction and properties of the generalized inverse.
SIAM J. Appl. Math., 15:269-272, 1967. BibTeX entry |
| [604] | W. Fleming. Functions of Several Variables (2nd edition).
Springer-Verlag, New York, 1977. BibTeX entry |
| [605] | R. Fletcher. Generalized inverse methods for the best least squares
solution of systems of non-linear equations. Comput. J., 10:392-399,
1968. BibTeX entry |
| [606] | R. Fletcher. A technique for orthogonalization. J. Inst. Math.
Appl., 5:162-166, 1969. BibTeX entry |
| [607] | R. Fletcher. Generalized inverses for nonlinear equations and
optimization, pages 75-85. In [1540]
, 1970. BibTeX entry |
| [608] | D. Flores de Chela. Generalized inverses on normed vector spaces.
Linear Algebra and its Applications, 26:243-263, 1979. BibTeX entry |
| [609] | D. Flores de Chela. Approximations in the l norm and the
generalized inverse. Linear Algebra and its Applications, 42:3-21,
1982. BibTeX entry |
| [610] | D. Flores de Chela. Generalized inverses under the l 1-norm.
Linear Algebra and its Applications, 94:237-261, 1987. BibTeX entry |
| [611] | N. Florsch and J. Hinderer. Bayesian estimation of the free core
nutation parameters from the analysis of precise tidal gravity data.
Physics of The Earth and Planetary Interiors, 117:21-35, 2000. BibTeX entry |
| [612] | A. Forsgren. On linear least-squares problems with diagonally dominant
weight matrices. SIAM J. Matrix Anal. Appl., 17(4):763-788, 1996. BibTeX entry |
| [613] | A. Forsgren and G. Sporre. On weighted linear least-squares problems
related to interior methods for convex quadratic programming. SIAM
J. Matrix Anal. Appl., 23:42-56, 2001. BibTeX entry |
| [614] | G. E. Forsythe. The maximum and minimum of a positive definite quadratic
polynomial on a sphere are convex functions of the radius. SIAM J.
Appl. Math., 19:551-554, 1970. BibTeX entry |
| [615] | G. E. Forsythe and G. H. Golub. On the stationary values of a second-degree
polynomial on the unit sphere. SIAM J. Appl. Math., 13:1050-1068,
1965. BibTeX entry |
| [616] | M. Foster. An application of the Wiener-Kolmogorov smoothing theory
to matrix inversion. J. Soc. Indust. Appl. Math., 9:387-392, 1961. BibTeX entry |
| [617] | D. J. Foulis. Baer -semigroups. Proc. Amer. Math. Soc.,
11:648-654, 1960. BibTeX entry |
| [618] | D. J. Foulis. Relative inverses in Baer*-semigroups.
Michigan Math. J., 10:65-84, 1963. BibTeX entry |
| [619] | J. S. Frame. Matrix functions and applications. I. matrix operations
and generalized inverses. IEEE Spectrum, 1:209-220, 1964. BibTeX entry |
| [620] | J. S. Frame. Matrix functions and applications. II. Functions of
a matrix. IEEE Spectrum, 1(4):102-108, 1964. BibTeX entry |
| [621] | J. S. Frame. Matrix functions and applications. IV. Matrix functions
and constituent matrices. IEEE Spectrum, 1(6):123-131, 1964. BibTeX entry |
| [622] | J. S. Frame. Matrix functions and applications. V. Similarity reductions
by rational or orthogonal matrices. IEEE Spectrum, 1(7):103-109,
1964. BibTeX entry |
| [623] | J. S. Frame and H. E. Koenig. Matrix functions and applications.
III. Applications of matrices to systems analysis. IEEE Spectrum
, 1(5):100-109, 1964. BibTeX entry |
| [624] | C. Franchetti and E. W. Cheney. Orthogonal projections in spaces
of continuous functions. J. Math. Anal. Appl., 63(1):253-264, 1978. BibTeX entry |
| [625] | P. Franck. Sur la distance minimale d'une matrice régulière
donnée au lieu des matrices singulières. In Deux. Congr.
Assoc. Franc. Calcul. et Trait. Inform. Paris 1961, pages 55-60. Gauthiers-Villars,
Paris, 1962. BibTeX entry |
| [626] | I. Fredholm. Sur une classe d'équations fonctionnelles.
Acta Math., 27:365-390, 1903. BibTeX entry |
| [627] | A. Friedlander, J. M. Martínez, and H. D. Scolnik. Generalized
inverses and a new stable secant type minimization algorithm. In Optimization
Techniques (Proc. 8th IFIP Conf., Würzburg, 1977), Part 2, pages
136-146. Lecture Notes in Control and Informat. Sci., Vol. 7. Springer,
Berlin, 1978. BibTeX entry |
| [628] | Masatoshi Fujii, Takayuki Furuta, and Ritsuo Nakamoto. Applications
of Gramian transformation formula. Sci. Math., 3(1):81-86 (electronic),
2000. BibTeX entry |
| [629] | J. D. Fulton. Generalized inverses of matrices over a finite field.
Discrete Math., 21(1):23-29, 1978. BibTeX entry |
| [630] | J. D. Fulton. Generalized inverses of matrices over fields of characteristic
two. Linear Algebra and its Applications, 28:69-76, 1979. BibTeX entry |
| [631] | R. E. Funderlic and C. D. Meyer, Jr. Sensitivity of the stationary
distribution vector for an ergodic Markov chain. Linear Algebra and
its Applications, 76:1-17, 1986. BibTeX entry |
| [632] | R. Gabriel. Extensions of generalized algebraic complement to arbitrary
matrices (romanian). Stud. Cerc. Mat., 17:1567-1581, 1965. BibTeX entry |
| [633] | R. Gabriel. Das verallgemeinerte Inverse einer Matrix deren Elemente
über einem beliebigen Körper angehören. J. Reine Angew.
Math., 234:107-122, 1969. BibTeX entry |
| [634] | R. Gabriel. Das verallgemeinerte Inverse einer Matrix über einem
beliebigen Körperanalytisch betrachtet. J. Reine Angew. Math.
, 244:83-93, 1970. BibTeX entry |
| [635] | R. Gabriel. Das verallgemeinerte Inverse einer Matrix über einen
beliebigen Körper-mit Skelettzerlegungen berechnet. Rev. Roumaine
Math. Pures Appl., 20:213-225, 1975. BibTeX entry |
| [636] | R. Gabriel. Das verallgemeinerte Inverse in Algebren. Rev. Roumaine
Math. Pures Appl., 20:311-324, 1975. (corrigendum: Rev. Roumaine Math.
Pures Appl. 20(1975), 747). BibTeX entry |
| [637] | R. Gabriel and R. E. Hartwig. The Drazin inverse as a gradient.
Linear Algebra and its Applications, 63:237-252, 1984. BibTeX entry |
| [638] | J. Gaches, J.-L. Rigal, and X. Rousset de Pina. Distance euclidienne
d'une application linéaire sigma au lieu des applications
de rang r donné. C. R. Acad. Sci. Paris, 260:5672-5674,
1965. BibTeX entry |
| [639] | A. Galántai. The theory of Newton's method. J. Comput.
Appl. Math., 124(1-2):25-44, 2000. (Numerical analysis 2000, Vol. IV,
Optimization and nonlinear equations). BibTeX entry |
| [640] | A. Galántai and G. Varga. A relaxation method for the computation
of generalized inverses of matrices. Közlemények-MTA Számitástechn.
Automat. Kutato Int. Budapest, (17):57-62, 1976. BibTeX entry |
| [641] | E. F. Galba. Weighted pseudo-inversion of matrices with singular
weights. Ukraï n. Mat. Zh., 46(10):1323-1327, 1994. BibTeX entry |
| [642] | E. F. Galba. Iterative methods for computing a weighted pseudo-inverse
matrix. Zh. Vychisl. Mat. i Mat. Fiz., 36(6):28-39, 1996. BibTeX entry |
| [643] | E. F. Galba. Representation of a weighted pseudo-inverse matrix in
terms of other pseudo-inverse matrices. Dopov. Nats. Akad. Nauk Ukr.
Mat. Prirodozn. Tekh. Nauki, (4):12-17, 1997. BibTeX entry |
| [644] | E. F. Galba, I. N. Molchanov, and V. V. Skopetski\i. Iterative methods
for computing a weighted pseudo-inverse matrix with singular weights.
Kibernet. Sistem. Anal., (5):150-169, 191, 1999. BibTeX entry |
| [645] | A. R. Gallant and T. M. Gerig. Computations for constrained linear
models. J. Econometrics, 12(1):59-84, 1980. (see
[431]
). BibTeX entry |
| [646] | A. M. Galperin and Z. Waksman. On pseudo-inverses of operator products.
Linear Algebra and its Applications, 33:123-131, 1980. BibTeX entry |
| [647] | A. M. Galperin and Z. Waksman. Ulm's method under regular smoothness.
Numer. Funct. Anal. Optim., 19(3-4):285-307, 1998. BibTeX entry |
| [648] | W. Gander. Algorithms for the polar decomposition. SIAM J. Sci.
Statist. Comput., 11(6):1102-1115, 1990. BibTeX entry |
| [649] | F. R. Gantmacher. The Theory of Matrices, volume I and II.
Chelsea, New York, 1959. BibTeX entry |
| [650] | Zhiqiang Gao and P. J. Antsaklis. Stability of the pseudo-inverse
method for reconfigurable control systems. Internat. J. Control
, 53(3):717-729, 1991. BibTeX entry |
| [651] | J. M. Garnett III, A. Ben-Israel, and S. S. Yau. A hyperpower iterative
method for computing matrix products involving the generalized inverse.
SIAM J. Numer. Anal., 8:104-109, 1971. BibTeX entry |
| [652] | M. K. Gavurin and Ju. B. Farforovskaja. An iterative method for finding
the minimum of sums of squares. Z. Vycisl. Mat. i Mat. Fiz., 6:1094-1097,
1966. BibTeX entry |
| [653] | D. M. Gay. Modifying singular values: existence of solutions to sytems
of nonlinear equations having a possibly singular Jacobian matrix.
Math. Comp., 31(140):962-973, 1977. BibTeX entry |
| [654] | D. M. Gay. Corrigenda: ``Modifying singular values: existence of
solutions to systems of nonlinear equations having a possibly singular
Jacobian matrix'' (Math. Comp. 31(1977), no. 140, 962-973).
Math. Comp., 33(145):432-433, 1979. BibTeX entry |
| [655] | A. George and Kh. D. Ikramov. Is the polar decomposition finitely
computable? SIAM J. Matrix Anal. Appl., 17(2):348-354, 1996. (see
[656]
). BibTeX entry |
| [656] | A. George and Kh. D. Ikramov. Addendum: ``Is the polar decomposition
finitely computable?'' [SIAM J. Matrix Anal. Appl. 17 (1996), no.
2, 348-354; MR 96m:15023]. SIAM J. Matrix Anal. Appl., 18(1):264,
1997. BibTeX entry |
| [657] | T. M. Gerig and A. R. Gallant. Computing methods for linear models
subject to linear parametric constraints. J. Statist. Comput. Simulation
, 3:283-296, 1975. (Errata: ibid 4 (1975), no. 1, 81-82). BibTeX entry |
| [658] | B. Germain-Bonne. Calcul de pseuodo-inverses. Rev. Francaise
Informat. Recherce Opérationelle, 3:3-14, 1969. BibTeX entry |
| [659] | A. J. Getson and F. C. Hsuan. {2}-Inverses and their Statistical
Application. Springer-Verlag, New York, 1988. BibTeX entry |
| [660] | C. Z. Gilstein and E. E. Leamer. The set of weighted regression estimates.
J. Amer. Statist. Assoc., 78(384):942-948, 1983. BibTeX entry |
| [661] | C. Giurescu and R. Gabriel. Some properties of the generalized matrix
inverse and semiinverse. An. Univ. Timisoara Ser. Sti. Mat.-Fiz. No.
, 2:103-111, 1964. BibTeX entry |
| [662] | I. M. Glazman and Ju. I. Ljubich. Finite Dimensional Linear Analysis
. Nauka, Moscow, 1969. (English translation published by MIT Press). BibTeX entry |
| [663] | S. Goldberg. Unbounded Linear Operators. McGraw-Hill Book
Co., New York, 1966. BibTeX entry |
| [664] | A. J. Goldman and M. Zelen. Weak generalized inverses and minimum
variance linear unbiased estimation. J. Res. Nat. Bur. Standards Sect.
B, 68B:151-172, 1964. BibTeX entry |
| [665] | A. A. Goldstein. Constructive Real Analysis. Harper and
Row, New York, 1967. BibTeX entry |
| [666] | G. R. Goldstein and J. A. Goldstein. The best generalized inverse.
J. Math. Anal. Appl., 252(1):91-101, 2000. BibTeX entry |
| [667] | M. J. Goldstein. Reduction of the pseudoinverse of a Hermitian persymmetric
matrix. Math. Comp., 28:715-717, 1974. BibTeX entry |
| [668] | M. Goldstein and A. F. M. Smith. Ridge-type estimators for regression
analysis. J. Roy. Statist. Soc. Ser. B, 36:284-291, 1974. BibTeX entry |
| [669] | H. Goller. Shorted operators and rank decomposition matrices.
Linear Algebra and its Applications, 81:207-236, 1986. BibTeX entry |
| [670] | G. H. Golub. Numerical methods for solving linear least squares problems.
Numer. Math., 7:206-216, 1965. BibTeX entry |
| [671] | G. H. Golub. Least squares, singular values and matrix approximations.
Aplikace Mathematiky, 13:44-51, 1968. BibTeX entry |
| [672] | G. H. Golub. Matrix decompositions and statistical calculations.
Tech. Report STAN-CS-124, Stanford University, Stanford, March 1969. BibTeX entry |
| [673] | G. H. Golub, M. T. Heath, and G. Wahba. Generalized cross-validation
as a method for choosing a good ridge parameter. Technometrics
, 21:215-223, 1979. BibTeX entry |
| [674] | G. H. Golub, A. J. Hoffman, and G. W. Stewart. A generalization of
the Eckart-Young-Mirsky matrix approximation theorem. Linear Algebra
and its Applications, 88/89:317-327, 1987. BibTeX entry |
| [675] | G. H. Golub and W. Kahan. Calculating the singular values and pseudo-inverse
of a matrix. J. Soc. Indust. Appl. Math. Ser. B Numer. Anal., 2:205-224,
1965. (see [465]
). BibTeX entry |
| [676] | G. H. Golub and C. D. Meyer, Jr. Using the QR factorization
and group inversion to compute, differentiate, and estimate the sensitivity
of stationary probabilities for Markov chains. SIAM J. Algebraic Discrete
Methods, 7(2):273-281, 1986. BibTeX entry |
| [677] | G. H. Golub and V. Pereyra. The differentiation of pseudoinverses
and nonlinear least squares problems whose variables separate. SIAM
J. Numer. Anal., 10:413-432, 1973. BibTeX entry |
| [678] | G. H. Golub and V. Pereyra. Differentiation of pseudoinverses, separable
nonlinear least squares problems and other tales. In Nashed
[1402]
, pages 303-324. BibTeX entry |
| [679] | G. H. Golub and C. Reinsch. Singular value decompositions and least
squares solutions. Numer. Math., 14:403-420, 1970. (republished,
pp. 134-151 in [2058]
). BibTeX entry |
| [680] | G. H. Golub and G. P. H. Styan. Numerical computations for univariate
linear models. Journal of Statistical Computations and Simulation
, 2:253-274, 1973. BibTeX entry |
| [681] | G. H. Golub and C. F. Van Loan. Matrix Computations. Johns
Hopkins University Press, Baltimore, MD, third edition, 1996. BibTeX entry |
| [682] | G. H. Golub and J. H. Wilkinson. Note on the iterative refinement
of least squares solutions. Numer. Math., 9:139-148, 1966. BibTeX entry |
| [683] | A. Gómez and D. Romeu. A pseudoinverse for Frank's formula.
Acta Cryst. Sect. A, 57(1):116-117, 2001. BibTeX entry |
| [684] | Xiangyang Gong, Wanyi Chen, and Fengsheng Tu. The stability and design
of nonlinear neural networks. Comput. Math. Appl., 35(8):1-7, 1998. BibTeX entry |
| [685] | C. C. Gonzaga and H. J. Lara. A note on properties of condition numbers.
Linear Algebra and its Applications, 261:269-273, 1997. (see
[942]
). BibTeX entry |
| [686] | I. J. Good. Some applications of the singular decomposition of a
matrix. Technometrics, 11:823-831, 1969. BibTeX entry |
| [687] | I. J. Good. Generalized determinants and generalized generalized
variance. J. Statist. Comput. Simulation, 12(3-4):311-315, 1980/81.
(see [153]
). BibTeX entry |
| [688] | M. C. Gouveia. Generalized invertibility of Hankel and Toeplitz matrices.
Linear Algebra and its Applications, 193:95-106, 1993. BibTeX entry |
| [689] | M. C. Gouveia. Group and Moore-Penrose invertibility of Bezoutians.
Linear Algebra and its Applications, 197/198:495-509, 1994. BibTeX entry |
| [690] | M. C. Gouveia and R. Puystjens. About the group inverse and Moore-Penrose
inverse of a product. Linear Algebra and its Applications, 150:361-369,
1991. BibTeX entry |
| [691] | B. Gramsch. Relative Inversion in der Störungstheorie von Operatoren
und psi -Algebren. Math. Ann., 269(1):27-71, 1984. BibTeX entry |
| [692] | P. R. Graves-Morris, D. E. Roberts, and A. Salam. The epsilon algorithm
and related topics. J. Comput. Appl. Math., 122(1-2):51-80, 2000. BibTeX entry |
| [693] | F. A. Graybill. An Introduction to Linear Statistical Models.
Vol I. McGraw-Hill Book Co., Inc., New York, 1961. BibTeX entry |
| [694] | F. A. Graybill. Theory and Application of the Linear Model
. Duxbury Press, North Scituate, Mass., 1976. BibTeX entry |
| [695] | F. A. Graybill. Matrices with Applications in Statistics.
Wadsworth Advanced Books and Software, Belmont, Calif., second edition,
1983. BibTeX entry |
| [696] | F. A. Graybill and G. Marsaglia. Idempotent matrices and quadratic
forms in the general linear hypothesis. Ann. Math. Statist., 28:678-686,
1957. BibTeX entry |
| [697] | F. A. Graybill, C. D. Meyer, Jr., and R. J. Painter. Note on the
computation of the generalized inverse of a matrix. SIAM Rev., 8:522-524,
1966. BibTeX entry |
| [698] | B. Green. The orthogonal approximation of an oblique structure in
factor analysis. Psychometrika, 17:429-440, 1952. BibTeX entry |
| [699] | W. L. Green and T. D. Morley. Operator means, norm convergence and
matrix functions. In Signal Processing, Scattering and Operator Theory,
and Numerical Methods (Amsterdam, 1989), pages 551-556. Birkhäuser
Boston, Boston, MA, 1990. BibTeX entry |
| [700] | W. L. Green and T. D. Morley. Operator means and matrix functions.
Linear Algebra and its Applications, 137/138:453-465, 1990. BibTeX entry |
| [701] | F. Greensite. Second-order approximation of the pseudoinverse for
operator deconvolutions and families of ill-posed problems. SIAM J.
Appl. Math., 59(1):1-16 (electronic), 1999. BibTeX entry |
| [702] | W. Greub and W. C. Rheinboldt. On a generalization of an inequality
of L. V. Kantorovich. Proc. Amer. Math. Soc., 10:407-415, 1959. BibTeX entry |
| [703] | W. Greub and W. C. Rheinboldt. Non self-adjoint boundary value problems
in ordinary differential equations. J. Res. Nat. Bur. Standards Sect.
B, 1960:83-90, 64B. BibTeX entry |
| [704] | T. N. E. Greville. On smoothing a finite table: A matrix approach.
J. Soc. Indust. Appl. Math., 5:137-154, 1957. BibTeX entry |
| [705] | T. N. E. Greville. The pseudoinverse of a rectangular matrix and
its application to the solution of systems of linear equations. SIAM
Rev., 1:38-43, 1959. BibTeX entry |
| [706] | T. N. E. Greville. Some applications of the pseudoinverse of a matrix.
SIAM Rev., 2:15-22, 1960. BibTeX entry |
| [707] | T. N. E. Greville. Note on fitting functions of several independent
variables. J. Soc. Indust. Appl. Math., 9:109-115, 1961. (Erratum,
ibid 9(1961), 317). BibTeX entry |
| [708] | T. N. E. Greville. Note on the generalized inverse of a matrix product.
J. Soc. Indust. Appl. Math., 9:109-115, 1966. BibTeX entry |
| [709] | T. N. E. Greville. Spectral generalized inverses of square matrices.
Math. Research Center Technical Summary Report 823, University of Wisconsin,
Madison, WI, October 1967. BibTeX entry |
| [710] | T. N. E. Greville. Some new generalized inverses with spectral properties.
In Boullion and Odell [255]
, pages 26-46. BibTeX entry |
| [711] | T. N. E. Greville. The Souriau-Frame algorithm and the Drazin pseudoinverse.
Linear Algebra and Appl., 6:205-208, 1973. BibTeX entry |
| [712] | T. N. E. Greville. Solutions of the matrix equation XAX =
X and relations between oblique and orthogonal projectors.
SIAM J. Appl. Math., 26:828-832, 1974. BibTeX entry |
| [713] | T. N. E. Greville and N. Keyfitz. Backward population projection
by a generalized inverse. In Computational Probability (Proc. Actuarial
Res. Conf., Brown Univ., Providence, R.I., 1975), pages 173-183.
Academic Press, New York, 1980. BibTeX entry |
| [714] | E. Griepentrog and R. März. Basic properties of some differential-algebraic
equations. Z. Anal. Anwendungen, 8(1):25-41, 1989. BibTeX entry |
| [715] | C. W. Groetsch. Steepest descent and least squares solvability.
Canad. Math. Bull., 17:275-276, 1974. BibTeX entry |
| [716] | C. W. Groetsch. A product integral representation of the generalized
inverse. Comment. Math. Univ. Carolinae, 16:13-20, 1975. BibTeX entry |
| [717] | C. W. Groetsch. Representations of the generalized inverse.
J. Math. Anal. Appl., 49:154-157, 1975. BibTeX entry |
| [718] | C. W. Groetsch. Generalized Inverses of Linear Operators: Representation
and Approximation. Monographs and Textbooks in Pure and Applied Mathematics,
No. 37. Marcel Dekker Inc., New York, 1977. BibTeX entry |
| [719] | C. W. Groetsch. The Forsythe-Motzkin method for singular linear operator
equations. J. Optim. Theory Appl., 25(2):311-315, 1978. BibTeX entry |
| [720] | C. W. Groetsch. On rates of convergence for approximations to the
generalized inverse. Numer. Funct. Anal. Optim., 1(2):195-201,
1979. BibTeX entry |
| [721] | C. W. Groetsch. Generalized inverses and generalized splines.
Numer. Funct. Anal. Optim., 2(1):93-97, 1980. (connection between generalized
inverses and generalized splines, see [1647]
). BibTeX entry |
| [722] | C. W. Groetsch. The Theory of Tikhonov Regularization for Fredholm
Equations of the First Kind. Pitman, London, 1984. BibTeX entry |
| [723] | C. W. Groetsch. Spectral methods for linear inverse problems with
unbounded operators. J. Approx. Theory, 70(1):16-28, 1992. BibTeX entry |
| [724] | C. W. Groetsch. Inclusions for the Moore-Penrose inverse with applications
to computational methods. In Contributions in Numerical Mathematics
, pages 203-211. World Sci. Publishing, River Edge, NJ, 1993. BibTeX entry |
| [725] | C. W. Groetsch. Inverse Problems in the Mathematical Sciences
. Friedr. Vieweg & Sohn, Braunschweig, 1993. BibTeX entry |
| [726] | C. W. Groetsch. Inclusions and identities for the Moore-Penrose inverse
of a closed linear operator. Math. Nachr., 171:157-164, 1995. BibTeX entry |
| [727] | C. W. Groetsch and J. Guacaneme. Arcangeli's method for Fredholm
equations of the first kind. Proc. Amer. Math. Soc., 99(2):256-260,
1987. BibTeX entry |
| [728] | C. W. Groetsch and M. Hanke. A general framework for regularized
evaluation of unstable operators. J. Math. Anal. Appl., 203(2):451-463,
1996. BibTeX entry |
| [729] | C. W. Groetsch and B. J. Jacobs. Iterative methods for generalized
inverses based on functional interpolation. In Campbell
[318]
, pages 220-232. BibTeX entry |
| [730] | C. W. Groetsch and J. T. King. Extrapolation and the method of regularization
for generalized inverses. J. Approx. Theory, 25(3):233-247, 1979. BibTeX entry |
| [731] | C. W. Groetsch and A. Neubauer. Regularization of ill-posed problems:
optimal parameter choice in finite dimensions. J. Approx. Theory
, 58(2):184-200, 1989. BibTeX entry |
| [732] | C. W. Groetsch and O. Scherzer. The optimal order of convergence
for stable evaluation of differential operators. Electronic J. Diff.
Eqtns., 1993(4):1-10, 1993. BibTeX entry |
| [733] | C. W. Groetsch and C. R. Vogel. Asymptotic theory of filtering for
linear operator equations with discrete noisy data. Math. Comp.
, 49(180):499-506, 1987. BibTeX entry |
| [734] | R. Grone. Certain isometries of rectangular complex matrices.
Linear Algebra and its Applications, 29:161-171, 1980. BibTeX entry |
| [735] | R. Grone, C. R. Johnson, E. M. Sa, and H. Wolkowicz. Normal matrices.
Linear Algebra and its Applications, 87:213-225, 1987. (characterizations
of normal matrices, continued in [555]
). BibTeX entry |
| [736] | J. Groß. Some remarks concerning the reverse order law.
Discuss. Math. Algebra Stochastic Methods, 17(2):135-141, 1997. BibTeX entry |
| [737] | J. Groß. Special generalized inverse matrices connected with
the theory of unified least squares. Linear Algebra and its Applications
, 264:325-327, 1997. BibTeX entry |
| [738] | J. Groß. A note on a partial ordering in the set of Hermitian
matrices. SIAM J. Matrix Anal. Appl., 18(4):887-892, 1997. BibTeX entry |
| [739] | J. Groß. More on concavity of a matrix function. SIAM
J. Matrix Anal. Appl., 19(2):365-368 (electronic), 1998. BibTeX entry |
| [740] | J. Groß. On contractions in linear regression. J. Statist.
Plann. Inference, 74(2):343-351, 1998. BibTeX entry |
| [741] | J. Groß. Solution to a rank equation. Linear Algebra and
its Applications, 289(1-3):127-130, 1999. BibTeX entry |
| [742] | J. Groß. Idempotency of the Hermitian part of a complex matrix.
Linear Algebra and its Applications, 289(1-3):135-139, 1999. BibTeX entry |
| [743] | J. Groß. On the product of orthogonal projectors. Linear
Algebra and its Applications, 289(1-3):141-150, 1999. BibTeX entry |
| [744] | J. Groß. A note on the rank-subtractivity ordering. Linear
Algebra and its Applications, 289(1-3):151-160, 1999. BibTeX entry |
| [745] | J. Groß. On oblique projection, rank additivity and the Moore-Penrose
inverse of the sum of two matrices. Linear and Multilinear Algebra
, 46(4):265-275, 1999. BibTeX entry |
| [746] | J. Groß. The Moore-Penrose inverse of a partitioned nonnegative
definite matrix. Linear Algebra and its Applications, 321(1-3):113-121,
2000. BibTeX entry |
| [747] | J. Groß. Nonnegative-definite and positive-definite solutions
to the matrix equation AXA =B-revisited.
Linear Algebra and its Applications, 321(1-3):123-129, 2000. BibTeX entry |
| [748] | J. Groß. Löwner partial ordering and space preordering
of Hermitian non-negative definite matrices. Linear Algebra and its
Applications, 326(1-3):215-223, 2001. BibTeX entry |
| [749] | J. Groß, J. Hauke, and A. Markiewicz. Some comments on matrix
partial orderings. Discuss. Math. Algebra Stochastic Methods, 17(2):203-214,
1997. BibTeX entry |
| [750] | J. Groß, J. Hauke, and A. Markiewicz. Partial orderings, preorderings,
and the polar decomposition of matrices. Linear Algebra and its Applications
, 289(1-3):161-168, 1999. BibTeX entry |
| [751] | J. Groß and S. Puntanen. Estimation under a general partitioned
linear model. Linear Algebra and its Applications, 321(1-3):131-144,
2000. BibTeX entry |
| [752] | J. Groß and G. Trenkler. On the least squares distance between
affine subspaces. Linear Algebra and its Applications, 237/238:269-276,
1996. BibTeX entry |
| [753] | J. Groß and G. Trenkler. Generalized and hypergeneralized projectors.
Linear Algebra and its Applications, 264:463-474, 1997. BibTeX entry |
| [754] | J. Groß and G. Trenkler. On the equality of usual and Amemiya's
partially generalized least squares estimator. Comm. Statist. Theory
Methods, 26(9):2075-2086, 1997. BibTeX entry |
| [755] | J. Groß and G. Trenkler. Restrictions and projections in linear
regression. Internat. J. Math. Ed. Sci. Tech., 28(3):465-468, 1997. BibTeX entry |
| [756] | J. Groß and G. Trenkler. On the product of oblique projectors.
Linear and Multilinear Algebra, 44(3):247-259, 1998. BibTeX entry |
| [757] | J. Groß and G. Trenkler. Nonsingularity of the difference of
two oblique projectors. SIAM J. Matrix Anal. Appl., 21(2):390-395
(electronic), 1999. BibTeX entry |
| [758] | J. Groß, G. Trenkler, and S. -O. Troschke. On semi-orthogonality
and a special class of matrices. Linear Algebra and its Applications
, 289(1-3):169-182, 1999. BibTeX entry |
| [759] | J. Groß and S. -O. Troschke. Some remarks on partial orderings
of nonnegative definite matrices. Linear Algebra and its Applications
, 264:457-461, 1997. BibTeX entry |
| [760] | M. Gruszczynski. The Moore-Penrose matrix inversion and estimation
under additional constraints. Przegl# ad Statyst., 28(3-4):311-319
(1982), 1981. BibTeX entry |
| [761] | Chuanqing Gu. Generalized inverse matrix Padé approximation
on the basis of scalar products. Linear Algebra and its Applications
, 322(1-3):141-167, 2001. BibTeX entry |
| [762] | J. Guacaneme and R. D. Ogden. On condition numbers and convergence
of the alternating projections method. Houston J. Math., 14(2):209-217,
1988. BibTeX entry |
| [763] | Zhi Hong Guan, Xiang Cai Wen, and Yong Qing Liu. Variation of the
parameters formula and the problem of BIBO for singular measure differential
systems with impulse effect. Appl. Math. Comput., 60(2-3):153-169,
1994. BibTeX entry |
| [764] | S. P. Gudder and M. Neumann. Splittings and iterative methods for
approximate solutions to singular operator equations in Hilbert spaces.
J. Math. Anal. Appl., 62(2):272-294, 1978. BibTeX entry |
| [765] | P. G. Guest. Orthogonal polynomials in the least squares fitting
of observations. Philos. Mag. (7), 41:124-137, 1950. BibTeX entry |
| [766] | E. A. Guillemin. Theory of Linear Physical Systems. Wiley,
New York, 1963. BibTeX entry |
| [767] | M. E. Gulliksson. On modified Gram-Schmidt for weighted and constrained
linear least squares. BIT, 35:458-473, 1995. BibTeX entry |
| [768] | M. E. Gulliksson, P.-Å. Wedin, and Yimin Wei. Perturbation
identities for regularized Tikhonov inverses and weighted pseudoinverses.
BIT, 40(3):513-523, 2000. BibTeX entry |
| [769] | N. N. Gupta. An iterative method for computation of generalized inverse
and matrix rank. IEEE Trans. Systems Man Cybernet., pages 89-90,
1971. BibTeX entry |
| [770] | N. N. Gupta. An optimum iterative method for the computation of matrix
rank. IEEE Trans. Systems Man Cybernet., pages 437-438, 1972. BibTeX entry |
| [771] | A. Guterman. Linear preservers for matrix inequalities and partial
orderings. Linear Algebra and its Applications, 331:75-87, 2001. BibTeX entry |
| [772] | A. Guterman. Linear preservers for Drazin star partial order.
Comm. in Algebra, 2001. BibTeX entry |
| [773] | T. Güyer, O. Kymaz, G. Bilgici, and S. Mirasyedioglu. A new
method for computing the solutions of differential equation systems using
generalized inverse via Maple. Appl. Math. Comput., 121(2-3):291-299,
2001. BibTeX entry |
| [774] | S. J. Haberman. How much do Gauss-Markov and least square estimates
differ? A coordinate-free approach. Ann. Statist., 3(4):982-990,
1975. (extension of [1093]
. BibTeX entry |
| [775] | F. J. Hall. Generalized inverses of a bordered matrix of operators.
SIAM J. Appl. Math., 29:152-163, 1975. BibTeX entry |
| [776] | F. J. Hall. On the independence of blocks of generalized inverses
of bordered matrices. Linear Algebra and Appl., 14(1):53-61, 1976. BibTeX entry |
| [777] | F. J. Hall and R. E. Hartwig. Further results on generalized inverses
of partitioned matrices. SIAM J. Appl. Math., 30(4):617-624, 1976. BibTeX entry |
| [778] | F. J. Hall and R. E. Hartwig. Algebraic properties of governing matrices
used in Cesàro-Neumann iterations. Rev. Roumaine Math. Pures
Appl., 26(7):959-978, 1981. BibTeX entry |
| [779] | F. J. Hall, R. E. Hartwig, I. J. Katz, and M. Newman. Pseudosimilarity
and partial unit regularity. Czechoslovak Math. J., 33(108)(3):361-372,
1983. BibTeX entry |
| [780] | F. J. Hall and I. J. Katz. On ranks of integral generalized inverses
of integral matrices. Linear and Multilinear Algebra, 7(1):73-85,
1979. BibTeX entry |
| [781] | F. J. Hall and I. J. Katz. More on integral generalized inverses
of integral matrices. Linear and Multilinear Algebra, 9(3):201-209,
1980. BibTeX entry |
| [782] | F. J. Hall and I. J. Katz. Nonnegative integral generalized inverses.
Linear Algebra and its Applications, 39:23-39, 1981. BibTeX entry |
| [783] | F. J. Hall and C. D. Meyer, Jr. Generalized inverses of the fundamental
bordered matrix used in linear estimation. Sankhya Ser. A, 37(3):428-438,
1975. (corrigendum in Sankhya Ser. A 40(1980), 399). BibTeX entry |
| [784] | C. R. Hallum, T. L. Boullion, and P. L. Odell. Best linear estimation
in the restricted general linear model. Indust. Math., 34(1):53-64,
1984. BibTeX entry |
| [785] | C. R. Hallum, T. O. Lewis, and T. L. Boullion. Estimation in the
restricted general linear model with a positive semidefinite covariance
matrix. Comm. Statist., 1:157-166, 1973. BibTeX entry |
| [786] | P. R. Halmos. Finite-Dimensional Vector Spaces. D. Van Nostrand,
Co., Princeton, 2nd edition, 1958. BibTeX entry |
| [787] | P. R. Halmos. A Hilbert Space Problem Book. D. Van Nostrand,
Co., Princeton, 1967. BibTeX entry |
| [788] | P. R. Halmos and J. E. McLaughlin. Partial isometries. Pacific
J. Math., 13:585-596, 1963. BibTeX entry |
| [789] | P. R. Halmos and L. J. Wallen. Powers of partial isometries.
J. Math. Mech., 19:657-663, 1970. BibTeX entry |
| [790] | I. Halperin. Closures and adjoints of linear differential operators.
Ann. of Math., pages 880-919, 1937. BibTeX entry |
| [791] | H. Hamburger. Non-symmetric operators in Hilbert space. In Proceedings
Symposium on Spectral Theory and Differential Problems, pages 67-112.
Oklahoma A& M College, Stillwater, OK, 1951. BibTeX entry |
| [792] | M. Hanke. Regularization with differential operators: an iterative
approach. Numer. Funct. Anal. Optim., 13(5-6):523-540, 1992. BibTeX entry |
| [793] | M. Hanke and M. Neumann. Preconditionings and splittings for rectangular
systems. Numerische Mathematik, 57(1):85-95, 1990. BibTeX entry |
| [794] | M. Hanke and M. Neumann. The geometry of the set of scaled projections.
Linear Algebra and its Applications, 190:137-148, 1993. BibTeX entry |
| [795] | M. Hanke and W. Niethammer. On the acceleration of Kaczmarz's method
for inconsistent linear systems. Linear Algebra and its Applications
, 130:83-98, 1990. BibTeX entry |
| [796] | G. W. Hansen and D. W. Robinson. On the existence of generalized
inverses. Linear Algebra and its Applications, 8:95-104, 1974. BibTeX entry |
| [797] | P. C. Hansen. The truncated SVD as a method for regularization.
BIT, 27:534-553, 1987. BibTeX entry |
| [798] | R. J. Hanson. A numerical method for solving Fredholm integral equations
of the first kind using singular values. SIAM J. Numer. Anal.,
8:616-622, 1971. BibTeX entry |
| [799] | R. J. Hanson and M. J. Norris. Analysis of measurements based on
the singular value decomposition. SIAM J. Sci. Statist. Comput.,
2(3):363-373, 1981. BibTeX entry |
| [800] | B. Harris. Theory of Probability. Addison-Wesley, Reading,
Mass., 1966. BibTeX entry |
| [801] | W. A. Harris, Jr. and T. N. Helvig. Applications of the pseudoinverse
to modeling. Technometrics, 8:351-357, 1966. BibTeX entry |
| [802] | R. Harte. Polar decomposition and the Moore-Penrose inverse.
Panamer. Math. J., 2(4):71-76, 1992. BibTeX entry |
| [803] | R. Harte and M. Mbekhta. On generalized inverses in C *-algebras.
Studia Math., 103(1):71-77, 1992. BibTeX entry |
| [804] | R. Harte and M. Mbekhta. Generalized inverses in C *-algebras.
II. Studia Math., 106(2):129-138, 1993. BibTeX entry |
| [805] | W. M. Hartmann and R. E. Hartwig. Computing the Moore-Penrose inverse
for the covariance matrix in constrained nonlinear estimation. SIAM
J. Optim., 6(3):727-747, 1996. BibTeX entry |
| [806] | J. Hartung. On a method for computing pseudoinverses. In Optimization
and Operations Research (Proc. Conf., Oberwolfach, 1975). Lecture Notes
in Econom. Math. Systems, Vol. 117, pages 115-125. Springer, Berlin,
1976. BibTeX entry |
| [807] | J. Hartung. Zur Darstellung pseudoinverser Operatoren. Arch.
Math. (Basel), 28(2):200-208, 1977. BibTeX entry |
| [808] | J. Hartung. A note on restricted pseudoinverses. SIAM J. Math.
Anal., 10(2):266-273, 1979. BibTeX entry |
| [809] | J. Hartung. Nonnegative minimum biased invariant estimation in variance
component models. Ann. Statist., 9(2):278-292, 1981. BibTeX entry |
| [810] | J. Hartung and H. -J. Werner. Zur Verwendung der restringierten Moore-Penrose-Inversen
beim Testen von linearen Hypothesen. Z. Angew. Math. Mech., 60(7):T344-T346,
1980. BibTeX entry |
| [811] | J. Hartung and H. -J. Werner. Hypothesenprüfung im restringierten
linearen Modell. Theorie und Anwendungen (With English and French summaries)
. Vandenhoeck & Ruprecht, Göttingen, 1984. BibTeX entry |
| [812] | R. E. Hartwig. 1-2 inverses and the invariance of BA
+C. Linear Algebra and its Applications, 11(3):271-275, 1975. BibTeX entry |
| [813] | R. E. Hartwig. AX-XB=C, resultants
and generalized inverses. SIAM J. Appl. Math., 28:154-183, 1975. BibTeX entry |
| [814] | R. E. Hartwig. Singular value decomposition and the Moore-Penrose
inverse of bordered matrices. SIAM J. Appl. Math., 31(1):31-41,
1976. BibTeX entry |
| [815] | R. E. Hartwig. More on the Souriau-Frame algorithm and the Drazin
inverse. SIAM J. Appl. Math., 31(1):42-46, 1976. BibTeX entry |
| [816] | R. E. Hartwig. Rank factorization and Moore-Penrose inversion.
Indust. Math., 26(1):49-63, 1976. BibTeX entry |
| [817] | R. E. Hartwig. Block generalized inverses. Arch. Rational Mech.
Anal., 61(3):197-251, 1976. BibTeX entry |
| [818] | R. E. Hartwig. Generalized inverses of special block matrices.
Bull. Calcutta Math. Soc., 69(6):397-402, 1977. BibTeX entry |
| [819] | R. E. Hartwig. Generalized inverses, EP elements and
associates. Rev. Roumaine Math. Pures Appl., 23(1):57-60, 1978. BibTeX entry |
| [820] | R. E. Hartwig. Spectral inverses and the row-space equations.
Linear Algebra and its Applications, 20(1):57-68, 1978. BibTeX entry |
| [821] | R. E. Hartwig. Schur's theorem and the Drazin inverse. Pacific
J. Math., 78(1):133-138, 1978. BibTeX entry |
| [822] | R. E. Hartwig. A note on the partial ordering of positive semidefinite
matrices. Linear and Multilinear Algebra, 6:223-226, 1978. BibTeX entry |
| [823] | R. E. Hartwig. A note on the existence of inner and outer inverses.
Math. Japon., 23(4):339-343, 1978/79. BibTeX entry |
| [824] | R. E. Hartwig. How to partially order regular elements. Math.
Japon., 25(1):1-13, 1980. BibTeX entry |
| [825] | R. E. Hartwig. An application of the Moore-Penrose inverse to antisymmetric
relations. Proc. Amer. Math. Soc., 78(2):181-186, 1980. BibTeX entry |
| [826] | R. E. Hartwig. A method for calculating Ad. Math.
Japon., 26(1):37-43, 1981. BibTeX entry |
| [827] | R. E. Hartwig. A note on rank additivity. Linear and Multilinear
Algebra, 10:59-61, 1981. BibTeX entry |
| [828] | R. E. Hartwig. Drazin inverses and canonical forms in M
n(z/h). Linear Algebra and its Applications, 37:205-233,
1981. BibTeX entry |
| [829] | R. E. Hartwig. Applications of the Wronskian and Gram matrices of
{tielambda kt}. Linear Algebra
and its Applications, 43:229-241, 1982. BibTeX entry |
| [830] | R. E. Hartwig. The reverse order law revisited. Linear Algebra
and its Applications, 76:241-246, 1986. BibTeX entry |
| [831] | R. E. Hartwig. The group inverse of a block triangular matrix.
In Current Trends in Matrix Theory (Auburn, Ala., 1986), pages 137-146.
North-Holland, New York, 1987. BibTeX entry |
| [832] | R. E. Hartwig. A remark on the characterization of the parallel sum
of two matrices. Linear and Multilinear Algebra, 22(2):193-197,
1987. BibTeX entry |
| [833] | R. E. Hartwig. The pyramid decomposition and rank minimization.
Linear Algebra and its Applications, 191:53-76, 1993. BibTeX entry |
| [834] | R. E. Hartwig. The weighted *-core-nilpotent decomposition.
Linear Algebra and its Applications, 211:101-111, 1994. BibTeX entry |
| [835] | R. E. Hartwig. EP perturbations. Sankhya Ser. A, 56(2):347-357,
1994. BibTeX entry |
| [836] | R. E. Hartwig and M. P. Drazin. Lattice properties of the * order
for matrices. J. Math. Anal. Appl., 86:359-378, 1982. BibTeX entry |
| [837] | R. E. Hartwig and F. J. Hall. Pseudo-similarity for matrices over
a field. Proc. Amer. Math. Soc., 71(1):6-10, 1978. BibTeX entry |
| [838] | R. E. Hartwig and F. J. Hall. Applications of the Drazin inverse
to Cesàro-Neumann iterations. In Campbell
[318]
, pages 145-195. BibTeX entry |
| [839] | R. E. Hartwig and I. J. Katz. On products of EP matrices. Linear
Algebra and its Applications, 252:339-345, 1997. BibTeX entry |
| [840] | R. E. Hartwig and J. Levine. Applications of the Drazin inverse to
the Hill cryptographic system. III. Cryptologia, 5(2):67-77, 1981. BibTeX entry |
| [841] | R. E. Hartwig and J. Levine. Applications of the Drazin inverse to
the Hill cryptographic system. IV. Cryptologia, 5(4):213-228,
1981. BibTeX entry |
| [842] | R. E. Hartwig and Jiang Luh. A note on the group structure of unit
regular ring elements. Pacific J. Math., 71(2):449-461, 1977. BibTeX entry |
| [843] | R. E. Hartwig and Jiang Luh. Unitary regular rings and partial isometry
rings. Math. Japon., 26(4):401-413, 1981. BibTeX entry |
| [844] | R. E. Hartwig and P. Semrl. Power additivity and orthogonality.
SIAM J. Matrix Anal. Appl., 20(1):1-13 (electronic), 1999. BibTeX entry |
| [845] | R. E. Hartwig and J. M. Shoaf. Group inverses and Drazin inverses
of bidiagonal and triangular Toeplitz matrices. J. Austral. Math.
Soc. Ser. A, 24(1):10-34, 1977. BibTeX entry |
| [846] | R. E. Hartwig and J. M. Shoaf. On the derivative of the Drazin inverse
of a complex matrix. SIAM J. Math. Anal., 10(1):207-216, 1979. BibTeX entry |
| [847] | R. E. Hartwig and J. M. Shoaf. Invariance, group inverses and parallel
sums. Rev. Roumaine Math. Pures Appl., 25(1):33-42, 1980. BibTeX entry |
| [848] | R. E. Hartwig and G. P. H. Styan. On some characterizations of the
star partial orderings and rank subtractivity. Linear Algebra and
its Applications, 82:145-161, 1986. BibTeX entry |
| [849] | R. E. Hartwig, M. Omladic, P. Semrl, and G. P. H. Styan. On some
characterizations of pairwise star ortogonality using rank and dagger additivity
and subtractivity. Linear Algebra and its Applications, 237-238:499-507,
1996. BibTeX entry |
| [850] | R. E. Hartwig, Guorong Wang, and Yimin Wei. Some additive results
on Drazin inverse. Linear Algebra and its Applications, 322(1-3):207-217,
2001. BibTeX entry |
| [851] | D. A. Harville. Extension of the Gauss-Markov theorem to include
the estimation of random effects. Ann. Statist., 4(2):384-395,
1976. BibTeX entry |
| [852] | D. A. Harville. Generalized inverses and ranks of modified matrices.
J. Indian Soc. Agricultural Statist., 49:67-78, iv, 1996/97. BibTeX entry |
| [853] | D. A. Harville. Matrix Algebra from a Statistician's Perspective
. Springer-Verlag, New York, 1997. BibTeX entry |
| [854] | W. R. Harwood, V. Lovass-Nagy, and D. L. Powers. A note on the generalized
inverses of some partitioned matrices. SIAM J. Appl. Math., 19:555-559,
1970. BibTeX entry |
| [855] | W. M. Häussler. Zu über- und unterrelaxierten Newton-Verfahren.
Z. Angew. Math. Mech., 58(7):T421-T423, 1978. BibTeX entry |
| [856] | D. M. Hawkins and D. Bradu. Application of the Moore-Penrose inverse
of a data matrix in multiple regression. Linear Algebra and its Applications
, 127:403-425, 1990. BibTeX entry |
| [857] | J. B. Hawkins and A. Ben-Israel. On generalized matrix functions.
Linear and Multilinear Algebra, 1(2):163-171, 1973. BibTeX entry |
| [858] | E. V. Haynsworth. Applications of an inequality for the Schur complement.
Proc. Amer. Math. Soc., 24:512-516, 1970. BibTeX entry |
| [859] | E. V. Haynsworth and J. R. Wall. Group inverses of certain nonnegative
matrices. Linear Algebra and its Applications, 25:271-288, 1979. BibTeX entry |
| [860] | E. V. Haynsworth and J. R. Wall. Group inverses of certain positive
operators. Linear Algebra and its Applications, 40:143-159, 1981. BibTeX entry |
| [861] | J. Hauke and A. Markiewicz. On partial orderings on the set of rectangular
matrices and their properties. Discuss. Math. Algebra Stochastic Methods
, 15(1):5-10, 1995. BibTeX entry |
| [862] | J. Hauke and A. Markiewicz. On partial orderings on the set of rectangular
matrices. Linear Algebra and its Applications, 219:187-193, 1995.
(see [1230]
). BibTeX entry |
| [863] | J. Z. Hearon. On the singularity of a certain bordered matrix.
SIAM J. Appl. Math., 15:1413-1421, 1967. BibTeX entry |
| [864] | J. Z. Hearon. Polar factorization of a matrix. J. Res. Nat.
Bur. Standards Sect. B, 71B:65-67, 1967. BibTeX entry |
| [865] | J. Z. Hearon. Construction of epr generalized
inverses by inversion of nonsingular matrices. J. Res. Nat. Bur. Standards
Sect. B, 71B:57-60, 1967. BibTeX entry |
| [866] | J. Z. Hearon. A generalized matrix version of Rennie's inequality.
J. Res. Nat. Bur. Standards Sect. B, 71B:61-64, 1967. BibTeX entry |
| [867] | J. Z. Hearon. Partially isometric matrices. J. Res. Nat. Bur.
Standards Sect. B, 71B:225-228, 1967. BibTeX entry |
| [868] | J. Z. Hearon. Symmetrizable generalized inverses of symmetrizable
matrices. J. Res. Nat. Bur. Standards Sect. B, 71B:229-231, 1967. BibTeX entry |
| [869] | J. Z. Hearon. Generalized inverses and solutions of linear systems.
J. Res. Nat. Bur. Standards Sect. B, 72B:303-308, 1968. BibTeX entry |
| [870] | J. Z. Hearon and J. W. Evans. On spaces and maps of generalized inverses.
J. Res. Nat. Bur. Standards Sect. B, 72B:103-107, 1968. BibTeX entry |
| [871] | J. Z. Hearon and J. W. Evans. Differentiable generalized inverses.
J. Res. Nat. Bur. Standards Sect. B, 72B:109-113, 1968. BibTeX entry |
| [872] | B. A. Hedman. An earlier date for ``Cramer's rule''. Historia
Math., 26(4):365-368, 1999. (Cramer's rule was discovered by Maclaurin
20 years earlier). BibTeX entry |
| [873] | C. Heil and D. Walnut. Continuous and discrete wavelet transforms.
SIAM Rev., 31:628-666, 1989. BibTeX entry |
| [874] | G. Heinig. The group inverse of the transformation S(X
)=AX-XB. Linear Algebra and its Applications
, 257:321-342, 1997. BibTeX entry |
| [875] | G. Heinig and F. Hellinger. On the Bezoutian structure of the Moore-Penrose
inverses of Hankel matrices. SIAM Journal on Matrix Analysis and Applications
, 14(3):629-645, 1993. BibTeX entry |
| [876] | G. Heinig and F. Hellinger. Displacement structure of generalized
inverse matrices. Linear Algebra and its Applications, 211:67-83,
1994. BibTeX entry |
| [877] | G. Heinig and F. Hellinger. Moore-Penrose inversion of square Toeplitz
matrices. SIAM Journal on Matrix Analysis and Applications, 15(2):418-450,
1994. BibTeX entry , http://epubs.siam.org/sam-bin/dbq/article/22585 |
| [878] | G. Heinig and F. Hellinger. Displacement structure of pseudoinverses.
Linear Algebra and its Applications, 197/198:623-649, 1994. BibTeX entry |
| [879] | G. Heinig and F. Hellinger. Displacement structure of generalized
inverse matrices. Linear Algebra and its Applications, 211:67-83,
1994. BibTeX entry |
| [880] | B. W. Helton. Logarithms of matrices. Proceedings of the American
Mathematical Society, 19:733-736, 1968. BibTeX entry |
| [881] | H. V. Henderson and S. R. Searle. The vec-permutation matrix, the
vec operator and Kronecker products: a review. Linear and Multilinear
Algebra, 9(4):271-288, 1980/81. BibTeX entry |
| [882] | H. V. Henderson and S. R. Searle. On deriving the inverse of a sum
of matrices. SIAM Rev., 23(1):53-60, 1981. BibTeX entry |
| [883] | G. P. Herring. A note on generalized interpolation and the pseudoinverse.
SIAM J. Numer. Anal., 4:548-556, 1967. BibTeX entry |
| [884] | M. R. Hestenes. Applications of the theory of quadratic forms in
Hilbert space to the calculus of variations. Pacific J. Math.,
1:525-581, 1951. BibTeX entry |
| [885] | M. R. Hestenes. Inversion of matrices by biorthogonalization and
related results. J. Soc. Indust. Appl. Math., 6:51-90, 1958. BibTeX entry |
| [886] | M. R. Hestenes. Relative Hermitian matrices. Pacific J. Math.
, 11:225-245, 1961. BibTeX entry |
| [887] | M. R. Hestenes. Relative self-adjoint operators in Hilbert space.
Pacific J. Math., 11:1315-1357, 1961. BibTeX entry |
| [888] | M. R. Hestenes. A ternary algelbra with applications to matrices
and linear transformations. Arch. Rational Mech. Anal., 11:138-194,
1962. BibTeX entry |
| [889] | M. R. Hestenes. On a ternary algebra. Scripta Math., 29:253-272,
1973. BibTeX entry |
| [890] | M. R. Hestenes. Pseudoinverses and conjugate gradients. Comm.
ACM, 18:40-43, 1975. BibTeX entry |
| [891] | K. R. Hickey and G. R. Luecke. Remarks on Marti's method for solving
first kind equations. SIAM J. Numer. Anal., 19(3):623-628, 1982. BibTeX entry |
| [892] | N. J. Higham. Computing the polar decomposition-with applications.
SIAM J. Sci. Statist. Comput., 7(4):1160-1174, 1986. BibTeX entry |
| [893] | N. J. Higham. Computing real square roots of a real matrix.
Linear Algebra and its Applications, 88/89:405-430, 1987. BibTeX entry |
| [894] | N. J. Higham. Computing a nearest symmetric positive semidefinite
matrix. Linear Algebra and Its Applications, 103:103-118, 1988. BibTeX entry |
| [895] | N. J. Higham and R. S. Schreiber. Fast polar decomposition of an
arbitrary matrix. SIAM J. Sci. Comput., 11(4):648-655, july 1990. BibTeX entry |
| [896] | D. Hilbert. Grundzüge einer algemeinen Theorie der linearen
Integralgleichungen. B. G. Teubner, Leipzig and Berlin, 1912. (Reprint
of six articles which appeared originally in the Götingen Nachrichten
(1904), 49-51; (1904), 213-259; (1905), 307-338; (1906), 157-227; (1906),
439-480; (1910), 355-417). BibTeX entry |
| [897] | T. H. Hildebrandt. On a theory of linear differential equations in
General Analysis. Trans. Amer. Math. Soc., 18:73-96, 1917. BibTeX entry |
| [898] | T. H. Hildebrandt. On bordered Fredholm determinants. Bull.
Amer. Math. Soc., 26:400-405, 1920. (see [487]
). BibTeX entry |
| [899] | J. W. Hilgers. On the equivalence of regularization and certain reproducing
kernel Hilbert space approaches for solving first kind problems. SIAM
J. Numer. Anal., 13(2):172-184, 1976. (see [900]
). BibTeX entry |
| [900] | J. W. Hilgers. Erratum: ``On the equivalence of regularization and
certain reproducing kernel Hilbert space approaches for solving first kind
problems'' (SIAM J. Numer. Anal. 13 (1976), no. 2, 172-184).
SIAM J. Numer. Anal., 15(6):1301, 1978. BibTeX entry |
| [901] | J. W. Hilgers. A note on estimating the optimal regularization parameter.
SIAM J. Numer. Anal., 17(3):472-473, 1980. BibTeX entry |
| [902] | J. W. Hilgers. A theory for optimal regularization in the finite-dimensional
case. Linear Algebra and its Applications, 48:359-379, 1982. BibTeX entry |
| [903] | H. W. Hodaway. GINV, A subroutine in ANSI fortran for generalized
matrix inversion. Australian Computer J., 9(4):159-161, 1977. BibTeX entry |
| [904] | B. L. Ho and R. E. Kalman. Effective construction of linear state-variables
models from input/output functions. Regelungstechnik, 14:545-548,
1966. BibTeX entry |
| [905] | Yu-chi Ho and R. L. Kashyap. A class of iterative procedures for
linear inequalities. SIAM J. Control, 4:112-115, 1966. BibTeX entry |
| [906] | A. E. Hoerl and R. W. Kennard. Ridge regression: Biased estimation
of nonorthogonal problems. Technometrics, 12:55-67, 1970. BibTeX entry |
| [907] | A. E. Hoerl and R. W. Kennard. A note on least squares estimates.
Communications in Statistics. Part B - Simulation and Computations
, 9:315-317, 1980. (generalization of [1785]
). BibTeX entry |
| [908] | A. E. Hoerl and R. W. Kennard. Ridge regression-1980. Advances, algorithms,
and applications. Amer. J. Math. Management Sci., 1(1):5-83, 1981. BibTeX entry |
| [909] | R. W. Hoerl. Ridge analysis 25 years later. Amer. Statist.
, 39(3):186-192, 1985. BibTeX entry |
| [910] | A. Holder. Desinging radiotherapy plans with elastic constraints
and interior point methods. Technical Report No. 49, Trinity University,
San Antonio, TX, 2000. BibTeX entry |
| [911] | A. G. Holder and R. J. Caron. Uniform bounds on the limiting and
marginal derivatives of the analytic center solution over a set of normalized
weights. Oper. Res. Lett., 26(2):49-54, 2000. BibTeX entry |
| [912] | A. Holder, J. Sturm, and S. Zhang. Marginal and parametric analysis
of the central optimal solution. Technical Report No. 48, Trinity University
Mathematics, 1999. (to appear in Information Systems and Operational Research). BibTeX entry |
| [913] | R. B. Holmes. A Course on Optimization and Best Approximation
. Springer-Verlag, Berlin, 1972. BibTeX entry |
| [914] | H. H. H. Homeier. Extrapolationsverfahren für Zahlen-, Vektor-
und Matrizenfolgen und ihre Anwendung in der Theoretischen und Physikalischen
Chemie. Habilitation thesis, Universität Regensburg, 1996. BibTeX entry , http://www.chemie.uni-regensburg.de/Theoretische_Chemie/Homeier/preprint/preprint.html#Homeier96Hab |
| [915] | H. H. H. Homeier. The vector J extrapolation method. In
Junping Wang, Myron B. Allen, III., Benito M. Chen, and Tarek Mathew, editors,
Iterative Methods in Scientific Computation, volume 4 of
IMACS Series in Computational and Applied Mathematics, pages 375-380.
IMACS, Dept. of Computer Science, Rutgers University, New Brunswick, NJ
08903, USA, 1998. Proceedings of the Third IMACS International Symposium
on Iterative Methods in Scientific Computation Jackson Hole, Wyoming, USA
- July 9-12, 1997. BibTeX entry , http://www.chemie.uni-regensburg.de/Theoretische_Chemie/Homeier/preprint/preprint.html#TC-NA-97-5 |
| [916] | R. A. Horn and C. R. Johnson. Matrix Analysis. Cambridge
University Press, Cambridge, 1985. (corrected reprint Cambridge University
Press, Cambridge, 1990). BibTeX entry |
| [917] | R. A. Horn and C. R. Johnson. Topics in Matrix Analysis.
Cambridge University Press, Cambridge, 1991. BibTeX entry |
| [918] | A. Höskuldsson. Data analysis, matrix decompositions, and generalized
inverse. SIAM J. Sci. Comput., 15(2):239-262, 1994. BibTeX entry |
| [919] | H. Hotelling. Relation between two sets of variates. Biometrika
, 28:322-377, 1936. BibTeX entry |
| [920] | H. Hotelling. Some new methods in matrix calculations. Annals
of Mathematical Statistics, 14:1-34, 1943. BibTeX entry |
| [921] | H. Hotelling. Relation of the newer multivariate statistical methods
to factor analysis. Br. J. Static. Psychol., 10:69-79, 1957. BibTeX entry |
| [922] | P. D. Hough and S. A. Vavasis. Complete orthogonal decomposition
for weighted least squares. SIAM J. Matrix Anal. Appl., 18(2):369-392,
1997. BibTeX entry |
| [923] | A. S. Householder. The Theory of Matrices in Numerical Analysis
. Blaisdell, New York, 1964. BibTeX entry |
| [924] | A. S. Householder. The Kantorovich and some related inequalities.
SIAM Rev., 7:463-473, 1965. BibTeX entry |
| [925] | A. S. Householder and G. Young. Matrix approximation and latent roots.
Amer. Math. Monthly, 45:165-171, 1938. BibTeX entry |
| [926] | F. C. Hsuan, P. Langenberg, and A. J. Getson. The {2}-inverse with
applications in statistics. Linear Algebra and its Applications,
70:241-248, 1985. BibTeX entry |
| [927] | K. Huang and J. Yu. Remarks on a formula for the pseudoinverse by
the modified Huang algorithm. Computing, 59(2):183-185, 1997. BibTeX entry |
| [928] | Liping Huang. The explicit solutions and solvability of linear matrix
equations. Linear Algebra and its Applications, 311(1-3):195-199,
2000. (see [291]
). BibTeX entry |
| [929] | C. H. Hung and T. L. Markham. The Moore-Penrose inverse of a partitioned
matrix M=(BA C0). Czechoslovak Math. J.
, 25(100)(3):354-361, 1975. BibTeX entry |
| [930] | C. H. Hung and T. L. Markham. The Moore-Penrose inverse of a sum
of matrices. J. Austral. Math. Soc. Ser. A, 24(4):385-392, 1977. BibTeX entry |
| [931] | M. F. Hurt and C. Waid. A generalized inverse which gives all the
integral solutions to a system of linear equations. SIAM J. Appl.
Math., 19:547-550, 1970. BibTeX entry |
| [932] | W. A. Hurwitz. On the pseudo-resolvent to the kernel of an integral
equation. Trans. Amer. Math. Soc., 13:405-418, 1912. BibTeX entry |
| [933] | D. Huylebrouck. The generalized inverse of a sum with radical element:
applications. Linear Algebra and its Applications, 246:159-175,
1996. BibTeX entry |
| [934] | D. Huylebrouck and R. Puystjens. Generalized inverses of a sum with
a radical element. Linear Algebra and its Applications, 84:289-300,
1986. BibTeX entry |
| [935] | D. Huylebrouck, R. Puystjens, and J. Van Geel. The Moore-Penrose
inverse of a matrix over a semisimple Artinian ring. Linear and Multilinear
Algebra, 16(1-4):239-246, 1984. BibTeX entry |
| [936] | D. Huylebrouck, R. Puystjens, and J. Van Geel. The Moore-Penrose
inverse of a matrix over a semi-simple Artinian ring with respect to an
involution. Linear and Multilinear Algebra, 23(3):269-276, 1988. BibTeX entry |
| [937] | I. Ichim. Sur le problème des moindres carrés.
C. R. Acad. Sci. Paris Sér. I Math., 326(5):625-627, 1998. BibTeX entry |
| [938] | I. Ichim. A new solution for the least squares problem. Int.
J. Comput. Math., 72(2):207-222, 1999. BibTeX entry |
| [939] | H. Idrissi, O. Lefebvre, and C. Michelot. Applications and numerical
convergence of the partial inverse method. In Optimization (Varetz,
1988), pages 39-54. Springer, Berlin, 1989. BibTeX entry |
| [940] | Y. Ijiri. On the generalized inverse of an incidence matrix.
J. Soc. Indust. Appl. Math., 13:941-945, 1965. BibTeX entry |
| [941] | Kh. D. Ikramov. The eigenvalues of a pseudoinverse matrix. Vestnik
Moskov. Univ. Ser. I Mat. Meh., 29(3):5-8, 1974. BibTeX entry |
| [942] | Kh. D. Ikramov. An algebraic proof of a result by Gonzaga and Lara.
Linear Algebra and its Applications, 299(1-3):191-194, 1999. BibTeX entry |
| [943] | I. C. F. Ipsen. An overview of relative theta theorems for
invariant subspaces of complex matrices. J. Comput. Appl. Math.
, 123(1-2):131-153, 2000. BibTeX entry |
| [944] | I. C. F. Ipsen. Absolute and relative perturbation bounds for invariant
subspaces of matrices. Linear Algebra and its Applications, 309(1-3):45-56,
2000. BibTeX entry |
| [945] | I. C. F. Ipsen and C. D. Meyer, Jr. The angle between complementary
subspaces. Amer. Math. Monthly, 102(10):904-911, 1995. BibTeX entry |
| [946] | I. C. F. Ipsen and C. D. Meyer, Jr. The idea behind Krylov methods.
Amer. Math. Monthly, 105(10):889-899, 1998. BibTeX entry |
| [947] | C. Itiki, R. E. Kalaba, and F. E. Udwadia. Appell's equations of
motion and the generalized inverse form. In Recent Trends in Optimization
Theory and Applications, pages 123-143. World Sci. Publishing, River
Edge, NJ, 1995. BibTeX entry |
| [948] | V. V. Ivanov and V. Yu. Kudrinskii. Approximate solution of linear
operator equations in Hilbert space by the method of least squares. I.
Zh. Vychisl. Mat. i Mat. Fiz., 6(5):831-841, 1966. BibTeX entry |
| [949] | Saichi Izumino. Convergence of generalized inverses and spline projectors.
J. Approx. Theory, 38(3):269-278, 1983. BibTeX entry |
| [950] | D. D. Jackson. Linear inverse theory with a priori data. In
Applied inverse problems, pages 83-102. Springer, Berlin, 1978. BibTeX entry |
| [951] | C. G. J. Jacobi. De formatione et proprietatibus determinantium.
Crelle Journal für die reine und angewandte Mathematik, 22:285-318,
1841. (reprinted in C.G.J. Jacobi's Gesammelte Werke (K. Weierstrass,
editor), Vol. 3, 355-392, Berlin 1884). BibTeX entry |
| [952] | C. G. J. Jacobi. De determinantibus functionalibus. Crelle Journal
für die reine und angewandte Mathematik, 22:319-359, 1841. (reprinted
in C.G.J. Jacobi's Gesammelte Werke (K. Weierstrass, editor), Vol.
3, 393-438, Berlin 1884). BibTeX entry |
| [953] | N. Jacobson. An application of E. H. Moore's determinant of a Hermitian
matrix. Bull. Amer. Math. Soc., 45:745-748, 1939. BibTeX entry |
| [954] | S. K. Jain. Nonnegative rectangular matrices having certain nonnegative
W-weighted group inverses. Proc. Amer. Math. Soc., 85(1):1-9,
1982. BibTeX entry |
| [955] | S. K. Jain, S. K. Mitra, and H. -J. Werner. Extensions of G
-based matrix partial orders. SIAM J. Matrix Anal. Appl., 17(4):834-850,
1996. BibTeX entry |
| [956] | D. James. Implicit nullspace iterative methods for constrained least
squares problems. SIAM J. Matrix. Anal. Appl., 13:962-978, 1992. BibTeX entry |
| [957] | S. R. Jammalamadaka and D. Sengupta. Changes in the general linear
model: a unified approach. Linear Algebra and its Applications,
289(1-3):225-242, 1999. BibTeX entry |
| [958] | P. A. Janakiraman and S. Renganathan. Recursive computation of pseudo-inverse
of matrices. Automatica-J. IFAC, 18(5):631-633, 1982. BibTeX entry |
| [959] | M. Jarnicki. A method of holomorphic retractions and pseudoinverse
matrices in the theory of continuation of delta-tempered functions.
Dissertationes Math. (Rozprawy Mat.), 258:50, 1987. BibTeX entry |
| [960] | D. R. Jensen. Minimal properties of Moore-Penrose inverses.
Linear Algebra and its Applications, 196:175-182, 1994. BibTeX entry |
| [961] | J. W. Jerome and L. L. Schumaker. A note on obtaining natural spline
functions by the abstract approach of Atteia and Laurent. SIAM J.
Numer. Anal., 5:657-663, 1968. BibTeX entry |
| [962] | M. W. Jeter and W. C. Pye. A note on nonnegative rank factorizations.
Linear Algebra and its Applications, 38:171-173, 1981. BibTeX entry |
| [963] | J. Ji. The algebraic perturbation method for generalized inverses.
J. Comput. Math., 7(4):327-333, 1989. BibTeX entry |
| [964] | J. Ji. An alternative limit expression of Drazin inverse and its
application. Appl. Math. Comput., 61(2-3):151-156, 1994. BibTeX entry |
| [965] | E. P. Jiang and M. W. Berry. Solving total least-squares problems
in information retrieval. Linear Algebra and its Applications, 316(1-3):137-156,
2000. BibTeX entry |
| [966] | Sheng Jiang. Angles between Euclidean subspaces. Geom. Dedicata
, 63(2):113-121, 1996. BibTeX entry |
| [967] | L. Jódar, A. G. Law, A. Rezazadeh, J. H. Weston, and G. Wu.
Computations for the Moore Penrose and other generalized inverses. In
Proceedings of the Twentieth Manitoba Conference on Numerical
Mathematics and Computing (Winnipeg, MB, 1990), volume 80, pages 57-64,
1991. BibTeX entry |
| [968] | J. A. John. Use of generalized inverse matrices in MANOVA. J.
Roy. Statist. Soc. Ser. B, 32:137-143, 1970. BibTeX entry |
| [969] | P. W. M. John. Pseudo-inverses in the analysis of variance.
Ann. Math. Statist., 35:895-896, 1964. BibTeX entry |
| [970] | C. R. Johnson, M. K. Kerr, and D. P. Stanford. Semipositivity of
matrices. Linear and Multilinear Algebra, 37(4):265-271, 1994.
(see [2045]
). BibTeX entry |
| [971] | C. R. Johnson, R. Loewy, D. D. Olesky, and P. van den Driessche.
Maximizing the spectral radius of fixed trace diagonal perturbations of
nonnegative matrices. Linear Algebra and its Applications, 241/243:635-654,
1996. BibTeX entry |
| [972] | Jon Jones, N. P. Karampetakis, and A. C. Pugh. The computation and
application of the generalized inverse via Maple. J. Symbolic Comput.
, 25(1):99-124, 1998. BibTeX entry |
| [973] | J. Jones, Jr. On the Lyapunov stability criteria. J. Soc. Indust.
Appl. Math., 13:941-945, 1965. BibTeX entry |
| [974] | J. Jones, Jr. Solution of certain matrix equations. Proc. Amer.
Math. Soc., 31:333-339, 1972. BibTeX entry |
| [975] | F. Jongmans. Resolution numérique de l'équation matricielle
AXB=C. Simon Stevin, 34:3-26,
1960/1961. BibTeX entry |
| [976] | F. Jongmans. Retour critique sur l'équation matricielle
AXB=C. In Hommage au Professeur Lucien Godeaux
, pages 127-134. Librairie Universitaire, Louvain, 1968. BibTeX entry |
| [977] | C. Jordan. Mémoires sur les formes bilinéaires.
J. Math. Pures Appl. Deuxième Sér., 19:35-54, 1874. (see
history of SVD in [1771]
). BibTeX entry |
| [978] | C. Jordan. Sur la réduction des formes bilinéaires.
C. R. de l'Acad. Sci. Paris, 78:614-617, 1874. (see history of
SVD in [1771]
). BibTeX entry |
| [979] | C. Jordan. Essai sur la géometry à n dimensions.
Bull. Soc. Math., 3:103-174, 1874. (see history of angles
in [1772]
). BibTeX entry |
| [980] | V. N. Joshi. Remarks on iterative methods for computing the generalised
inverse. Studia Sci. Math. Hungar., 8:457-461, 1973. BibTeX entry |
| [981] | V. N. Joshi. A determinant for rectangular matrices. Bull. Austral.
Math. Soc., 21(1):137-146, 1980. BibTeX entry |
| [982] | V. N. Joshi and R. P. Tewarson. On solving ill-conditioned systems
of linear equations. Trans. New York Acad. Sci. (2), 34:565-571,
1972. BibTeX entry |
| [983] | D. G. Kabe. On unified singular least squares theory. Indust.
Math., 35(2):97-104, 1985. BibTeX entry |
| [984] | S. Kaczmarz. Angenäherte Auflösung von Systemen linearer
Gleichungen. Bulletin de l'Académie Polonaise des Sciences
et Lettres, A35:355-357, 1937. BibTeX entry |
| [985] | D. G. Kaffes. An inequality for matrices. Bull. Soc. Math. Grèce
(N.S.), 22:143-159, 1981. BibTeX entry |
| [986] | D. G. Kaffes, T. Mathew, M. Bhaskara Rao, and K. Subramanyam. On
the matrix convexity of the Moore-Penrose inverse and some applications.
Linear and Multilinear Algebra, 24(4):265-271, 1989. BibTeX entry |
| [987] | W. Kahan. Huge generalized inverses of rank-defficient matrices
. University of Calfornia at Berkley, 2001. (online lecture notes). BibTeX entry , http://www.cs.berkeley.edu/~wkahan/MathH110/gilite.pdf |
| [988] | R. Kala. Projectors and linear estimation in general linear models.
Comm. Statist. A-Theory Methods, 10(9):849-873, 1981. BibTeX entry |
| [989] | R. E. Kalaba and F. E. Udwadia. On constrained motion. Appl.
Math. Comput., 51(1):85-86, 1992. BibTeX entry |
| [990] | R. E. Kalaba and F. E. Udwadia. Lagrangian mechanics, Gauss' principle,
quadratic programming, and generalized inverses: new equations for non-holonomically
constrained discrete mechanical systems. Quart. Appl. Math., 52(2):229-241,
1994. BibTeX entry |
| [991] | R. E. Kalaba, F. E. Udwadia, and R. Xu. Constrained motion revisited.
Appl. Math. Comput., 70(1):67-76, 1995. BibTeX entry |
| [992] | R. E. Kalaba, F. E. Udwadia, R. Xu, and C. Itiki. The equivalence
of Lagrange's equations of motion of the first kind and the generalized
inverse form. Nonlinear World, 2(4):519-526, 1995. BibTeX entry |
| [993] | R. E. Kalaba and Rong Xu. On the generalized inverse form of the
equations of constrained motion. Amer. Math. Monthly, 102(9):821-825,
1995. BibTeX entry |
| [994] | S. Kakutani. Some characterizations of Euclidean spaces. Japan
J. Math., 16:93-97, 1939. BibTeX entry |
| [995] | C. Kallina. A Green's function approach to perturbations of periodic
solutions. Pacific J. Math., 29:325-334, 1969. BibTeX entry |
| [996] | R. E. Kalman. Contributions to the theory of optimal control.
Bol. Soc. Mat. Mexicana, 5(2):102-119, 1960. BibTeX entry |
| [997] | R. E. Kalman. A new approach to linear filtering and prediction problems.
Trans. ASME Ser. D. J. Basic Eng., 82:35-45, 1960. BibTeX entry |
| [998] | R. E. Kalman. New results in linear filtering and prediction problems.
Trans. ASME Ser. D. J. Basic Eng., 83:95-107, 1961. BibTeX entry |
| [999] | R. E. Kalman. Mathematical description of linear dynamical systems.
SIAM J. Control, 1:152-192, 1963. BibTeX entry |
| [1000] | R. E. Kalman. Algebraic aspects of the generalized inverses of a
rectangular matrix. In M. Z. Nashed, editor, Generalized Inverses
and Applications (Proc. Sem., Math. Res. Center, Univ. Wisconsin, Madison,
Wis., 1973), pages 189-213. Academic Press, New York, 1976. BibTeX entry |
| [1001] | R. E. Kalman, Y. C. Ho, and K. S. Narendra. Controllability of linear
dynamical systems. In Contributions to Differential Equations, Vol.
I, pages 189-213. Interscience, New York, 1963. BibTeX entry |
| [1002] | B. Kaltenbacher. Some Newton-type methods for the regularization
of nonlinear ill-posed problems. Inverse Problems, 13(3):729-753,
1997. BibTeX entry |
| [1003] | W. J. Kammerer and M. Z. Nashed. Steepest descent for singular linear
operators with nonclosed range. Applicable Anal., 1(2):143-159,
1971. BibTeX entry |
| [1004] | W. J. Kammerer and M. Z. Nashed. A generalization of a matrix iterative
method of g. cimmino to best approximate solution of linear integral equations
of the first kind. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat.
Natur. (8), 51:20-25, 1971. BibTeX entry |
| [1005] | W. J. Kammerer and M. Z. Nashed. Iterative methods for best approximate
solutions of linear integral equations of the first and second kinds.
J. Math. Anal. Appl., 40:547-573, 1972. BibTeX entry |
| [1006] | W. J. Kammerer and M. Z. Nashed. On the convergence of the conjugate
gradient method for singular linear operator equations. SIAM J. Numer.
Anal., 9:165-181, 1972. BibTeX entry |
| [1007] | L. V. Kantorovich and G. P. Akilov. Functional Analysis in Normed
Spaces. Pergamon Press, Oxford, 1964. (translated from Russian). BibTeX entry |
| [1008] | L. V. Kantorovich and V. I. Krylov. Approximate Methods of Higher
Analysis. Interscience, New York, 1958. (translated from Russian). BibTeX entry |
| [1009] | N. P. Karampetakis. Computation of the generalized inverse of a polynomial
matrix and applications. Linear Algebra and its Applications,
252:35-60, 1997. BibTeX entry |
| [1010] | N. P. Karampetakis. Generalized inverses of two-variable polynomial
matrices and applications. Circuits Systems Signal Process., 16(4):439-453,
1997. BibTeX entry |
| [1011] | I. Karasalo. A criterion for truncation of the QR-decomposition
algorithm for the singular linear least squares problem. Nordisk Tidskr.
Informationsbehandling (BIT), 14:156-166, 1974. BibTeX entry |
| [1012] | S. Kass. Spaces of closest fit. Linear Algebra and its Applications
, 117:93-97, 1989. BibTeX entry |
| [1013] | Yoshinobu Kato and Nobuhiro Moriya. Maeda's inequality for pseudoinverses.
Math. Japon., 22(1):89-91, 1977. BibTeX entry |
| [1014] | A. K. Katsaggelos and S. N. Efstratiadis. A class of iterative signal
restoration algorithms. IEEE Trans. Acoust. Speech Signal Process.
, 38(5):778-786, 1990. BibTeX entry |
| [1015] | I. J. Katz. Wiegmann type theorems for EPr matrices.
Duke Math. J., 32:423-427, 1965. BibTeX entry |
| [1016] | I. J. Katz. Remarks on a paper of Ben-Israel. SIAM J. Appl.
Math., 18:511-513, 1970. BibTeX entry |
| [1017] | I. J. Katz and M. H. Pearl. On EPr and normal
EPr matrices. J. Res. Nat. Bur. Standards
Sect. B, 70B:47-77, 1966. BibTeX entry |
| [1018] | I. J. Katz and M. H. Pearl. Solutions of the matrix equation A
=XA=AX. J. London Math. Soc., 41:443-452,
1966. BibTeX entry |
| [1019] | L. Kaufman and V. Pereyra. A method for separable nonlinear least
squares problems with separable nonlinear equality constraints. SIAM
J. Numer. Anal., 15(1):12-20, 1978. BibTeX entry |
| [1020] | H. B. Keller. On the solution of singular and semidefinite linear
systems by iteration. SIAM Journal on Numerical Analysis, 2:281-290,
1965. BibTeX entry |
| [1021] | S. Keller-McNulty and W. J. Kennedy. Error-free computation of the
Moore-Penrose inverse with application to linear least squares analysis.
J. Statist. Comput. Simulation, 27(1):45-64, 1987. BibTeX entry |
| [1022] | J. D. Kelly. A regularization approach to the reconciliation of constrained
data sets. Computers & Chemical Engineering, 22:1771-1788,
1998. BibTeX entry |
| [1023] | I. M. Khabaza. An iterative least-square method suitable for solving
large sparse matrices. Comput. J., 6:202-206, 1963/1964. BibTeX entry |
| [1024] | V. G. Khajdukov, V. I. Kostin, and V. A. Tcheverda. The r-solution
and its applications in linearized waveform inversion for a layered background.
In Inverse Problems in Wave Propagation (Minneapolis, MN, 1995)
, pages 277-294. Springer, New York, 1997. BibTeX entry |
| [1025] | C. G. Khatri. A theorem on least squares in multivariate linear regression.
J. Amer. Statist. Assoc., 62:1494-1495, 1967. BibTeX entry |
| [1026] | C. G. Khatri. A note on some results on a generalised inverse of
a matrix. J. Indian Statist. Assoc., 7:38-45, 1969. BibTeX entry |
| [1027] | C. G. Khatri. A note on a commutative g-inverse of a matrix.
Sankhya Ser. A, 32:299-310, 1970. BibTeX entry |
| [1028] | C. G. Khatri. A representation of a matrix and its use in the Gauss-Markoff
model. J. Indian Statist. Assoc., 20:89-98, 1982. BibTeX entry |
| [1029] | C. G. Khatri. A generalization of Lavoie's inequality concerning
the sum of idempotent matrices. Linear Algebra and its Applications
, 54:97-108, 1983. BibTeX entry |
| [1030] | C. G. Khatri. A note on idempotent matrices. Linear Algebra
and its Applications, 70:185-195, 1985. BibTeX entry |
| [1031] | C. G. Khatri. Commutative g-inverse of a matrix. Math.
Today, 3:37-40, 1985. BibTeX entry |
| [1032] | C. G. Khatri. Study of redundancy of vector variables in canonical
correlations. Comm. Statist. Theory Methods, 18(4):1425-1440, 1989. BibTeX entry |
| [1033] | C. G. Khatri and S. K. Mitra. Hermitian and nonnegative solutions
of linear matrix equations. SIAM J. Appl. Math., 31:579-585, 1976. BibTeX entry |
| [1034] | C. G. Khatri and C. R. Rao. Some extensions of the Kantorovich inequality
and statistical applications. J. Multivariate Anal., 11(4):498-505,
1981. BibTeX entry |
| [1035] | B. D. Kiekebusch-Müller. A class of algorithms for the determination
of a solution of a system of nonlinear equations. In Optimization
Techniques (Proc. 8th IFIP Conf., Würzburg, 1977), Part 2, pages
67-75. Lecture Notes in Control and Informat. Sci., Vol. 7. Springer, Berlin,
1978. BibTeX entry |
| [1036] | Byung Chun Kim and Jang Taek Lee. The Moore-Penrose inverse for the
classificatory models. J. Korean Statist. Soc., 15(1):46-61, 1986. BibTeX entry |
| [1037] | Doh-Hyun Kim and Jun-Ho Oh. The Moore-Penrose inverse for the classificatory
models. Control Engineering Practice, 7(3):369-373, 1999. BibTeX entry |
| [1038] | S. Kim. Generalized inverses in numerical solutions of Cauchy singular
integral equations. Commun. Korean Math. Soc., 13(4):875-888,
1998. BibTeX entry |
| [1039] | S. Kim. Solving singular integral equations using Gaussian quadrature
and overdetermined system. Comput. Math. Appl., 35(10):63-71,
1998. BibTeX entry |
| [1040] | S. Kim. Numerical solutions of cauchy singular integral equations
using generalized inverses. Computers & Mathematics with Applications
, 38(5-6):183-195, 1999. BibTeX entry |
| [1041] | Chen F. King. A note on Drazin inverses. Pacific J. Math.
, 70(2):383-390, 1977. BibTeX entry |
| [1042] | M. J. L. Kirby. Generalized Inverses and Chance Constrained
Programming. Applied math., Northwestern Univ., Evanston, IL, June
1965. BibTeX entry |
| [1043] | N. F. Kirichenko. Analytical representation of perturbations of pseudo-inverse
matrices. Kibernet. Sistem. Anal., (2):98-107, 189, 1997. (English
translation: Cybernet. Systems Anal. 33 (1997), no. 2, 230-238). BibTeX entry |
| [1044] | S. J. Kirkland. The group inverse associated with an irreducible
periodic nonnegative matrix. SIAM J. Matrix Anal. Appl., 16(4):1127-1134,
1995. BibTeX entry |
| [1045] | S. J. Kirkland and M. Neumann. Convexity and concavity of the Perron
root and vector of Leslie matrices with applications to a population model.
SIAM J. Matrix Anal. Appl., 15(4):1092-1107, 1994. BibTeX entry |
| [1046] | S. J. Kirkland and M. Neumann. Group inverses of M-matrices
associated with nonnegative matrices having few eigenvalues. Linear
Algebra and its Applications, 220:181-213, 1995. BibTeX entry |
| [1047] | S. J. Kirkland and M. Neumann. The M-matrix group generalized
inverse problem for weighted trees. SIAM J. Matrix Anal. Appl.
, 19(1):226-234 (electronic), 1998. BibTeX entry |
| [1048] | S. J. Kirkland and M. Neumann. On group inverses of M-matrices
with uniform diagonal entries. Linear Algebra and its Applications
, 296(1-3):153-170, 1999. BibTeX entry |
| [1049] | S. J. Kirkland and M. Neumann. Cutpoint decoupling and first passage
times for random walks on graphs. SIAM J. Matrix Anal. Appl.,
20(4):860-870 (electronic), 1999. BibTeX entry |
| [1050] | S. J. Kirkland and M. Neumann. Regular Markov chains for which the
transition matrix has large exponent. Linear Algebra and its Applications
, 316(1-3):45-65, 2000. BibTeX entry |
| [1051] | S. J. Kirkland and M. Neumann. Extremal first passage times for trees.
Linear and Multilinear Algebra, 48:21-33, 2000. BibTeX entry |
| [1052] | S. J. Kirkland, M. Neumann, and B. L. Shader. Distances in weighted
trees and group inverse of Laplacian matrices. SIAM J. Matrix Anal.
Appl., 18(4):827-841, 1997. BibTeX entry |
| [1053] | S. J. Kirkland, M. Neumann, and B. L. Shader. Bounds on the subdominant
eigenvalue involving group inverses with applications to graphs. Czechoslovak
Math. J., 48(123)(1):1-20, 1998. BibTeX entry |
| [1054] | S. J. Kirkland, M. Neumann, and B. L. Shader. On a bound on algebraic
connectivity: the case of equality. Czechoslovak Math. J., 48(123)(1):65-76,
1998. BibTeX entry |
| [1055] | S. J. Kirkland, M. Neumann, and B. L. Shader. Applications of Paz's
inequality to perturbation bounds for Markov chains. Linear Algebra
and its Applications, 268:183-196, 1998. BibTeX entry |
| [1056] | F. H. Kishi. On line computer control techniques and their application
to re-entry aerospace vehicle control. In Advances in Control Systems
Theory and Applications (C. T. Leondes, Editor), pages 245-257. Academic
Press, New York, 1964. BibTeX entry |
| [1057] | N. M. Kislovskaya. A pseudo-inverse matrix and multiplicative groups
of matrices. In Algorithmic and Numerical Problems in Algebra and
Number Theory (Russian), pages 40-52, 88. Akad. Nauk SSSR Dal' nevostochn.
Otdel., Vladivostok, 1987. BibTeX entry |
| [1058] | V. Klee. Review of `linearity of best approximations: A characterization
of ellipsoids' (Rudin and Smith). Math. Reviews, 23:A2028, 1962. BibTeX entry |
| [1059] | A. Klinger. Approximate pseudoinverse solutions to ill-conditioned
linear systems. J. Optimization Th. Appl., 2:117-128, 1968. BibTeX entry |
| [1060] | A. V. Knyazev and M. E. Argentati. An effective and robust algorithm
for finding principal angles between subspaces using an A-based scalar
product. Technical Report 163, Center for Computational Mathematics,
University of Colorado at Denver, August 2000. BibTeX entry |
| [1061] | M. Koecher. The generalized inverse of integral matrices. Linear
Algebra and its Applications, 71:187-198, 1985. BibTeX entry |
| [1062] | E. G. Kogbetliantz. Solution of linear systems by diagonalization
of coefficients matrix. Quarterly of Applied Mathematics, 13:123-132,
1955. BibTeX entry |
| [1063] | J. J. Koliha. Pseudo-inverses of operators. Bull. Amer. Math.
Soc., 80:325-328, 1974. BibTeX entry |
| [1064] | J. J. Koliha. Power convergence and pseudoinverses of operators in
Banach spaces. J. Math. Anal. Appl., 48:446-469, 1974. BibTeX entry |
| [1065] | J. J. Koliha. The product of relatively regular operators. Comment.
Math. Univ. Carolinae, 16(3):531-539, 1975. BibTeX entry |
| [1066] | J. J. Koliha. A generalized Drazin inverse. Glasgow Math. J.
, 38(3):367-381, 1996. BibTeX entry |
| [1067] | J. J. Koliha. A simple proof of the product theorem for EP matrices.
Linear Algebra and its Applications, 294(1-3):213-215, 1999. BibTeX entry |
| [1068] | J. J. Koliha. The Drazin and Moore-Penrose inverse in C
-algebras. Math. Proc. R. Ir. Acad., 99A(1):17-27, 1999. BibTeX entry |
| [1069] | J. J. Koliha. Elements of C -algebras commuting with their
Moore-Penrose inverse. Studia Math., 139(1):81-90, 2000. BibTeX entry |
| [1070] | J. J. Koliha. Continuity and differentiability of the Moore-Penrose
inverse in C -algebras. Math. Scand., 88(1):154-160, 2001. BibTeX entry |
| [1071] | J. J. Koliha. Range projections of idempotents in C -algebras.
Demonstratio Math., 34(1):91-103, 2001. BibTeX entry |
| [1072] | J. J. Koliha. Block diagonalization. Math. Bohem., 126(1):237-246,
2001. BibTeX entry |
| [1073] | J. J. Koliha. Error bounds for a general perturbation of the Drazin
inverse. Appl. Math. Comput., 126(2-3):61-65, 2002. BibTeX entry |
| [1074] | J. J. Koliha and V. Rakocevic. Continuity of the Drazin inverse.
II. Studia Math., 131(2):167-177, 1998. BibTeX entry |
| [1075] | J. J. Koliha and I. Straskraba. Power bounded and exponentially bounded
matrices. Appl. Math., 44(4):289-308, 1999. BibTeX entry |
| [1076] | J. J. Koliha and T. D. Tran. Semistable operators and singularly
perturbed differential equations. J. Math. Anal. Appl., 231(2):446-458,
1999. BibTeX entry |
| [1077] | A. Korányi. Around the finite-dimensional spectral theorem.
Amer. Math. Monthly, 108:120-125, 2001. BibTeX entry |
| [1078] | A. Korganoff and M. Pavel-Parvu. Méthodes de calcul numérique.
Tome II: Éléments de théorie des matrices carrées
et rectangles en analyse numérique. Dunod, Paris, 1967. BibTeX entry |
| [1079] | V. M. Korsukov. An application of iteration methods to the computation
of semi-inverses of matrices. In Optimization Methods and Operations
Research, Applied Mathematics (Russian), pages 171-173, 191. Akad.
Nauk SSSR Sibirsk. Otdel. Sibirsk. Ènerget. Inst., Irkutsk, 1976. BibTeX entry |
| [1080] | V. M. Korsukov. Some properties of generalized inverse matrices.
In Degenerate Systems of Ordinary Differential Equations, pages
19-37. ``Nauka'' Sibirsk. Otdel., Novosibirsk, 1982. BibTeX entry |
| [1081] | M. Koshy and R. P. Tewarson. On the use of restricted pseudo-inverses
for the unified derivation of quasi-Newton updates. IMA J. Numer.
Anal., 5(2):141-151, 1985. BibTeX entry |
| [1082] | V. I. Kostin, V. G. Khajdukov, and V. A. Tcheverda. On r-solutions
of nonlinear equations. In Advanced Mathematics: Computations and Applications
(Novosibirsk, 1995), pages 286-291. NCC Publ., Novosibirsk, 1995. BibTeX entry |
| [1083] | V. I. Kostin, V. G. Khajdukov, and V. A. Tcheverda. r-solutions
of equations of the first kind with a compact operator in Hilbert spaces:
existence and stability. Dokl. Akad. Nauk, 355(3):308-312, 1997. BibTeX entry |
| [1084] | S. Kourouklis and C. C. Paige. A constrained least squares approach
to the general Gauss-Markov linear model. J. Amer. Statist. Assoc.
, 76(375):620-625, 1981. BibTeX entry |
| [1085] | O. Krafft. An arithmetic-harmonic-mean inequality for nonnegative
definite matrices. Linear Algebra and its Applications, 268:243-246,
1998. BibTeX entry |
| [1086] | W. Krajewski. Aggregation of models with restricted domains: an application
of the pseudo-inverses. In Large Scale Systems: Theory and Applications
1983 (Warsaw, 1983), pages 201-205. IFAC, Laxenburg, 1984. BibTeX entry |
| [1087] | R. G. Kreijger and H. Neudecker. Exact linear restrictions on parameters
in the general linear model with a singular covariance matrix. J.
Amer. Statist. Assoc., 72(358):430-432, 1977. BibTeX entry |
| [1088] | M. G. Kre\in. The theory of self-adjoint extensions of semi-bounded
Hermitian transformations and its applications. I. Rec. Math. [Mat.
Sbornik] N.S., 20(62):431-495, 1947. BibTeX entry |
| [1089] | M. G. Kre\in. The theory of self-adjoint extensions of semi-bounded
Hermitian transformations and its applications. II. Mat. Sbornik N.S.
, 21(63):365-404, 1947. BibTeX entry |
| [1090] | R. Kress. On the Fredholm alternative. Integral Equations Operator
Theory, 6(3):453-457, 1983. BibTeX entry |
| [1091] | E. V. Krishnamurthy. Fast parallel exact computation of the Moore-Penrose
inverse and rank of a matrix. Elektron. Informationsverarb. Kybernet.
, 19(1-2):95-98, 1983. BibTeX entry |
| [1092] | W. Kruskal. The coordinate-free approach to Gauss-Markov estimation,
and its application to missing and extra observations. In Proc. 4th
Berkeley Sympos. Math. Statist. and Prob., Vol. I, pages 435-451. Univ.
California Press, Berkeley, Calif., 1961. BibTeX entry |
| [1093] | W. Kruskal. When are Gauss-Markov and least squares estimators identical?
A coordinate-free approach. Ann. Math. Statist, 39:70-75, 1968.
(see [774]
). BibTeX entry |
| [1094] | W. Kruskal. The geometry of generalized inverses. J. Roy. Statist.
Soc. Ser. B, 37:272-283, 1975. (correction in J. Roy. Statist. Soc.
Ser. B48(1986), 258). BibTeX entry |
| [1095] | Jiao Xun Kuang. The representation and approximation of Drazin inverses
of linear operators. Numer. Math. J. Chinese Univ., 4(2):97-106,
1982. BibTeX entry |
| [1096] | Jiao Xun Kuang. Approximate methods for generalized inverses of operators
in Banach spaces. J. Comput. Math., 11(4):323-328, 1993. BibTeX entry |
| [1097] | V. N. Kublanovskaya. On the calculation of generalized inverses and
projections (Russian). Z. Vycisl. Mat. i Mat. Fiz., 6:326-332,
1966. BibTeX entry |
| [1098] | H. W. Kuhn, editor. Proceedings Princeton Sympos. Math. Prog.
, Princeton, NJ, 1970. Princeton Univ. Press. BibTeX entry |
| [1099] | S. H. Kulkarni and K. C. Sivakumar. Applications of generalized inverses
to interval linear programs in Hilbert spaces. Numer. Funct. Anal.
Optim., 16(7-8):965-973, 1995. BibTeX entry |
| [1100] | S. H. Kulkarni and K. C. Sivakumar. Explicit solutions of a special
class of linear programming problems in Banach spaces. Acta Sci. Math.
(Szeged), 62(3-4):457-465, 1996. BibTeX entry |
| [1101] | P. Kunkel and V. Mehrmann. Generalized inverses of differential-algebraic
operators. SIAM J. Matrix Anal. Appl., 17(2):426-442, 1996. BibTeX entry |
| [1102] | I Wen Kuo. The Moore-Penrose inverses of singular M-matrices.
Linear Algebra and Appl., 17(1):1-14, 1977. BibTeX entry |
| [1103] | M. C. Y. Kuo and L. F. Mazda. Mimimum energy problems in Hilbert
function space. J. Franklin Inst., 283:38-54, 1967. BibTeX entry |
| [1104] | S. Kurepa. Generalized inverse of an operator with a closed range.
Glasnik Mat., 3(23):207-214, 1968. BibTeX entry |
| [1105] | B. Kutzler and V. Kokol-Voljc. Introduction to Derive 5.
Texas Instruments, Dallas, TX 75265, 2000. BibTeX entry , http://education.ti.com/product/pdf/gb/derive5bk.pdf |
| [1106] | C. D. LaBudde and G. R. Verma. On the computation of a generalized
inverse of a matrix. Quart. Appl. Math., 27:391-395, 1969. BibTeX entry |
| [1107] | B. F. Lamond. An efficient factorization for the group inverse.
SIAM J. Algebraic Discrete Methods, 8(4):797-808, 1987. BibTeX entry |
| [1108] | B. F. Lamond. A generalized inverse method for asymptotic linear
programming. Math. Programming, 43(1 (Ser. A)):71-86, 1989. BibTeX entry |
| [1109] | B. F. Lamond and M. L. Puterman. Generalized inverses in discrete
time Markov decision processes. SIAM J. Matrix Anal. Appl., 10(1):118-134,
1989. BibTeX entry |
| [1110] | P. Lancaster. Explicit solutions of linear matrix equations.
SIAM Rev., 12:544-566, 1970. BibTeX entry |
| [1111] | P. Lancaster. A fundamental theorem on lambda-matrices with applications-I.
ordinary differential equations with constant coefficients. Linear
Algebra and its Applications, 18:189-211, 1977. BibTeX entry |
| [1112] | P. Lancaster. A fundamental theorem on lambda-matrices with applications-II.
difference equations with constant coefficients. Linear Algebra and
its Applications, 18:213-222, 1977. BibTeX entry |
| [1113] | P. Lancaster and J. G. Rokne. Solutions of nonlinear operator equations.
SIAM Journal on Mathematical Analysis, 8:448-457, 1977. BibTeX entry |
| [1114] | P. Lancaster and M. Tismenetsky. The Theory of Matrices (Second
Edition). Academic Press, San Diego, 1985. BibTeX entry |
| [1115] | C. Lanczos. Linear systems in self-adjoint form. Amer. Math.
Monthly, 65:665-679, 1958. BibTeX entry |
| [1116] | C. Lanczos. Linear Differential Operators. D. Van Nostrand,
Co., Princeton, 1961. BibTeX entry |
| [1117] | E. M. Landesman. Hilbert-space methods in elliptic partial differential
equations. Pacific J. Math., 21:113-131, 1967. BibTeX entry |
| [1118] | P. M. Lang, J. M. Brenchley, R. G. Nieves, and J. H. Kalivas. Cyclic
subspace regression. J. Multivariate Anal., 65(1):58-70, 1998. BibTeX entry |
| [1119] | C. E. Langenhop. On generalized inverses of matrices. SIAM J.
Appl. Math., 15:1239-1246, 1967. BibTeX entry |
| [1120] | C. E. Langenhop. The Laurent expansion for a nearly singular matrix.
Linear Algebra and its Applications, 4:329-340, 1971. BibTeX entry |
| [1121] | C. E. Langenhop. On the invertibiliby of a nearly singular matrix.
Linear Algebra and its Applications, 7:361-365, 1973. BibTeX entry |
| [1122] | L. J. Lardy. A series representation for the generalized inverse
of a closed linear operator. Atti Accad. Naz. Lincei Rend. Cl. Sci.
Fis. Mat. Natur. (8), 58(2):152-157, 1975. BibTeX entry |
| [1123] | L. J. Lardy. Some iterative methods for linear operator equations
with applications to generalized inverses. SIAM J. Appl. Math.
, 32(3):610-618, 1977. BibTeX entry |
| [1124] | W. E. Larimore. Order-recursive factorization of the pseudoinverse
of a covariance matrix. IEEE Trans. Automat. Control, 35(12):1299-1303,
1990. BibTeX entry |
| [1125] | Ty A. Lasky and B. Ravani. Sensor-based path planning and motion
control for a robotic system for roadway crack sealing. IEEE Transactions
on Control Systems Technology, 8:609-622, 2000. BibTeX entry |
| [1126] | K. J. Latawiec, S. Banka, and J. Tokarzewski. Control zeros and nonminimum
phase lti mimo systems. Annual Reviews in Control, 24(1):105-112,
2000. BibTeX entry |
| [1127] | P. -J. Laurent. Approximation et Optimisation. Collection Enseignement
des Sciences, No. 13. Hermann, Paris, 1972. BibTeX entry |
| [1128] | P. -J. Laurent. Quadratic convex analysis and splines. In Methods
of Functional Analysis in Approximation Theory (Bombay, 1985), pages
17-43. Birkhäuser, Basel, 1986. BibTeX entry |
| [1129] | K. B. Laursen and M. Mbekhta. Closed range multipliers and generalized
inverses. Studia Math., 107(2):127-135, 1993. BibTeX entry |
| [1130] | J. -L. Lavoie. A determinantal inequality involving the Moore-Penrose
inverse. Linear Algebra and its Applications, 31:77-80, 1980. BibTeX entry |
| [1131] | C. L. Lawson and R. J. Hanson. Solving Least Squares Problems
. Prentice-Hall Inc., Englewood Cliffs, N.J., 1974. (reprinted, Classics
in Applied Mathematics, 15. Society for Industrial and Applied Mathematics
(SIAM), Philadelphia, PA, 1995. xii+337 pp). BibTeX entry |
| [1132] | E. B. Leach. A note on inverse function theorems. Proc. Amer.
Math. Soc., 12:694-697, 1961. BibTeX entry |
| [1133] | E. B. Leach. On a related function theorem. Proc. Amer. Math.
Soc., 14:687-689, 1963. BibTeX entry |
| [1134] | E. E. Leamer. Coordinate-free ridge regression bounds. J. Amer.
Statist. Assoc., 76(376):842-849, 1981. BibTeX entry |
| [1135] | E. E. Leamer. Errors in variables in linear systems. Econometrica
, 55(4):893-909, 1987. BibTeX entry |
| [1136] | G. G. Lendaris, K. Mathia, and R. Saeks. Linear Hopfield networks
and constrained optimization. IEEE Transactions on Systems, Man, and
Cybernetics, Part B: Cybernetics, 29:114-118, 1999. BibTeX entry |
| [1137] | G. -S. Leng and Y. Zhang. Vertex angles for simplices. Applied
Mathematics Letters, 12:1-5, 1999. BibTeX entry |
| [1138] | A. H. Lent. Wiener-Hopf Operators and Factorizations. Doctoral
dissertation in applied mathematics, Northwestern Univertsity, Evanston,
IL, June 1971. BibTeX entry |
| [1139] | A. S. Leonov. Approximate calculation of a pseudo-inverse matrix
by means of the generalized residual principle. Zh. Vychisl. Mat.
i Mat. Fiz., 25(6):933-935, 959, 1985. BibTeX entry |
| [1140] | A. S. Leonov. The method of a minimal pseudoinverse matrix for solving
ill-posed problems of linear algebra. Dokl. Akad. Nauk SSSR, 285(1):36-40,
1985. (English translation: Soviet Math. Dokl. 32(1985), no. 3,
628-632). BibTeX entry |
| [1141] | A. S. Leonov. The method of a minimal pseudoinverse matrix.
Zh. Vychisl. Mat. i Mat. Fiz., 27(8):1123-1138, 1276, 1987. BibTeX entry |
| [1142] | A. S. Leonov. On the theory of the method of the minimal pseudo-inverse
matrix. Dokl. Akad. Nauk SSSR, 314(1):89-93, 1990. BibTeX entry |
| [1143] | A. S. Leonov. The minimal pseudo-inverse matrix method: theory and
numerical realization. Zh. Vychisl. Mat. i Mat. Fiz., 31(10):1427-1443,
1991. BibTeX entry |
| [1144] | A. S. Leonov. On the accuracy of the minimal pseudo-inverse matrix
method. Mat. Zametki, 49(4):81-87, 158, 1991. BibTeX entry |
| [1145] | A. S. Leonov. The method of minimal pseudoinversed matrix. Basic
statements. In Ill-Posed Problems in Natural Sciences (Moscow, 1991)
, pages 57-62. VSP, Utrecht, 1992. BibTeX entry |
| [1146] | Ö. Leringe and P.-Å. Wedin. A comparison between different
methods to compute a vector which minimizes A-b2
when G=h. Department of computer science, Lund University,
Lund, Sweden, March 1970. BibTeX entry |
| [1147] | G. Lesnjak. Semigroups of EP linear transformations. Linear
Algebra and its Applications, 304(1-3):109-118, 2000. BibTeX entry |
| [1148] | Y. Levin and A. Ben-Israel. Directional Newton methods in n
variables. Mathematics of Computations, 2001. BibTeX entry , http://rutcor.rutgers.edu/~bisrael/NEWTON-DIR.ps |
| [1149] | Y. Levin and A. Ben-Israel. A Newton method for systems of m
equations in n variables. Nonlinear Analysis, 47:1961-1971,
2001. BibTeX entry , ftp://rutcor.rutgers.edu/pub/rrr/reports2000/26.ps |
| [1150] | Y. Levin and A. Ben-Israel. Directional Halley and quasi-Halley methods
in n variables. In D. Butnariu, Y. Censor, and S. Reich, editors,
Inherently Parallel Algorithms in Feasibility and Optimization
and their Applications, Amsterdam, 2001. Elsevier Science. BibTeX entry , ftp://rutcor.rutgers.edu/pub/rrr/reports2000/28.ps |
| [1151] | Y. Levin and A. Ben-Israel. The Newton bracketing method for convex
minimization. Computational Optimization and Applications, 21:213-229,
2002. BibTeX entry , ftp://rutcor.rutgers.edu/pub/rrr/reports2000/33.ps |
| [1152] | Y. Levin and A. Ben-Israel. Inverse-free methods for systems of nonlinear
equations. RUTCOR-Rutgers Ctr. Oper. Res. 58-2000, Rutgers University,
Piscataway, NJ, 2000. BibTeX entry , ftp://rutcor.rutgers.edu/pub/rrr/reports2000/58.ps |
| [1153] | Y. Levin, M. Nediak, and A. Ben-Israel. A direct approach to calculus
of variations via Newton-Raphson method. Comput. & Appl. Math.
, 139:197-213, 2001. BibTeX entry |
| [1154] | J. Levine and R. E. Hartwig. Applications of the Drazin inverse to
the Hill cryptographic system. I. Cryptologia, 4(2):71-85, 1980. BibTeX entry |
| [1155] | J. Levine and R. E. Hartwig. Applications of the Drazin inverse to
the Hill cryptographic system. II. Cryptologia, 4(3):150-168,
1980. BibTeX entry |
| [1156] | B. C. Levy. A note on the hyperbolic singular value decomposition.
Linear Algebra and its Applications, 277(1-3):135-142, 1998. BibTeX entry |
| [1157] | A. S. Lewis. The convex analysis of unitarily invariant matrix functions.
J. Convex Anal., 2(1-2):173-183, 1995. BibTeX entry |
| [1158] | T. O. Lewis, T. L. Boullion, and P. L. Odell. A bibliography on generalized
matrix inverses. In Boullion and Odell [255]
, pages 283-315. BibTeX entry |
| [1159] | T. O. Lewis and T. G. Newman. Pseudoinverses of positive semidefinite
matrices. SIAM J. Appl. Math., 16:701-703, 1968. BibTeX entry |
| [1160] | T. O. Lewis and P. L. Odell. A generalization of the Gauss-Markov
theorem. J. Amer. Statist. Assoc., 61:1063-1066, 1966. BibTeX entry |
| [1161] | Bin Li, Yinghui Li, and Xuegang Ying. Dynamic modeling and simulation
of flexible cable with large sag. Applied Mathematics and Mechanics
(English Edition), 21:707-714, 2000. BibTeX entry |
| [1162] | Chi-Kwong Li and R. Mathias. Extremal characterizations of the Schur
complement and resulting inequalities. SIAM Rev., 42(2):233-246
(electronic), 2000. BibTeX entry |
| [1163] | Chi-Kwong Li and Nam-Kiu Tsing. Some isometries of rectangular complex
matrices. Linear and Multilinear Algebra, 23(1):47-53, 1988. BibTeX entry |
| [1164] | Ren Cang Li. Norms of certain matrices with applications to variations
of the spectra of matrices and matrix pencils. Linear Algebra and
its Applications, 182:199-234, 1993. BibTeX entry |
| [1165] | Ren-Cang Li. A perturbation bound for the generalized polar decomposition.
BIT, 33(2):304-308, 1993. BibTeX entry |
| [1166] | Ren-Cang Li. Relative perturbation theory. III. More bounds on eigenvalue
variation. Linear Algebra and its Applications, 266:337-345, 1997. BibTeX entry |
| [1167] | Ren-Cang Li. Relative perturbation theory. I. Eigenvalue and singular
value variations. SIAM J. Matrix Anal. Appl., 19(4):956-982 (electronic),
1998. BibTeX entry |
| [1168] | Ren-Cang Li. Relative perturbation theory. II. Eigenspace and singular
subspace variations. SIAM J. Matrix Anal. Appl., 20(2):471-492
(electronic), 1999. BibTeX entry |
| [1169] | Ren-Cang Li. Relative perturbation theory. IV. 2theta theorems.
Linear Algebra and its Applications, 311(1-3):45-60, 2000. BibTeX entry |
| [1170] | Ren-Cang Li and G. W. Stewart. A new relative perturbation theorem
for singular subspaces. Linear Algebra and its Applications, 313(1-3):41-51,
2000. BibTeX entry |
| [1171] | Xiezhang Li and Yimin Wei. An improvement on the perturbation of
the group inverse and oblique projection. Linear Algebra and its Applications
, 338:53-66, 2001. BibTeX entry |
| [1172] | Ping Liang, Su Huan Chen, and Cheng Huang. Moore-Penrose inverse
method of topological variation of finite element systems. Comput.
& Structures, 62(2):243-251, 1997. BibTeX entry |
| [1173] | Yi Liang and Xue Rong Yong. Group inverses of block matrices.
J. Xinjiang Univ. Natur. Sci., 9(4):34-39, 1992. BibTeX entry |
| [1174] | A. E. Liber. On the theory of generalized groups. Doklady Akad.
Nauk SSSR (N.S.), 97:25-28, 1954. BibTeX entry |
| [1175] | D. K. Lika. The application of generalized inverse operators in iteration
processes. Mat. Issled., 10(2(36)):264-270, 289, 1975. BibTeX entry |
| [1176] | Shwu-Yeng T. Lin and You Feng Lin. The n-dimensional Pythagorean
theorem. Linear and Multilinear Algebra, 26(1-2):9-13, 1990. (see
[202]
). BibTeX entry |
| [1177] | K. -W. Lin and A. R. Sanford. Improving regional earthquake locations
using a modified G matrix and fuzzy logic. Bulletin of the Seismological
Society of America, 91(1-2):82-93, 2001. BibTeX entry |
| [1178] | E. P. Liski. On Löwner-ordering antitonicity of matrix inversion.
Acta Math. Appl. Sinica (English Ser.), 12(4):435-442, 1996. BibTeX entry |
| [1179] | E. P. Liski and S. Puntanen. A further note on a theorem on the difference
of the generalized inverses of two nonnegative definite matrices.
Comm. Statist. Theory Methods, 18(5):1747-1751, 1989. BibTeX entry |
| [1180] | E. P. Liski and Song Gui Wang. Another look at the naive estimator
in a regression model. Metrika, 41(1):55-64, 1994. BibTeX entry |
| [1181] | E. P. Liski and Song Gui Wang. On the {2}-inverse and some ordering
properties of nonnegative definite matrices. Acta Math. Appl. Sinica
(English Ser.), 12(1):22-27, 1996. BibTeX entry |
| [1182] | W. G. Lister. Ternary rings. Trans. Amer. Math. Soc., 154:37-55,
1971. BibTeX entry |
| [1183] | Jianzhou Liu and Jian Wang. Some inequalities for Schur complements.
Linear Algebra and its Applications, 293(1-3):233-241, 1999. BibTeX entry |
| [1184] | X. Liu and D. Liu. Recursive computation of generalized inverses
with application to optimal state estimation. Control Theory Adv.
Tech., 10:1485-1497, 1995. BibTeX entry |
| [1185] | J. Locker. An existence analysis for nonlinear equations in Hilbert
space. Trans. Amer. Math. Soc., 128:403-413, 1967. BibTeX entry |
| [1186] | J. Locker. An existence analysis for nonlinear boundary value problems.
SIAM J. Appl. Math., 19:199-207, 1970. BibTeX entry |
| [1187] | A. T. Lonseth. Approximate solutions of Fredholm-type integral equations.
Bull. Amer. Math. Soc., 60:415-430, 1954. BibTeX entry |
| [1188] | Jesús López Estrada and Valia Guerra Ones. Numerical
calculation of the pseudoinverse using Leonov's minimal method. Investigación
Oper., 17(1-3):139-147, 1996. BibTeX entry |
| [1189] | Jesús López Estrada and Valia Guerra Ones. Maximum
balance criterion for choosing the parameter lambda in the minimal
pseudoinverse method. Revista Investigación Operacional,
21, 2000. BibTeX entry |
| [1190] | Jesús López Estrada, Humberto Madrid de la Vega, and
Valia Guerra Ones. Numerical calculation of the Moore-Penrose pseudoinverse
of a matrix. Investigación Oper., 17(1-3):117-132, 1996. BibTeX entry |
| [1191] | W. S. Loud. Some singular cases of the implicit function theorem.
Amer. Math. Monthly, 68:965-977, 1961. BibTeX entry |
| [1192] | W. S. Loud. Generalized inverses and generalized Green's functions.
SIAM J. Appl. Math., 14:342-369, 1966. BibTeX entry |
| [1193] | W. S. Loud. Some examples of generalized Green's functions and generalized
Green's matrices. SIAM Rev., 12:194-210, 1970. BibTeX entry |
| [1194] | W. S. Loud. A bifurcation application of the generalized inverse
of a linear differential operator. SIAM J. Math. Anal., 11(3):545-558,
1980. BibTeX entry |
| [1195] | V. Lovass-Nagy, R. J. Miller, and D. L. Powers. On system realization
by matrix generalized inverses. Internat. J. Control, 26(5):745-751,
1977. (see correction in [547]
). BibTeX entry |
| [1196] | V. Lovass-Nagy and D. L. Powers. On the commuting reciprocal inverse
of some partitioned matrices. Linear Algebra and its Applications
, 4:183-190, 1971. BibTeX entry |
| [1197] | V. Lovass-Nagy and D. L. Powers. A relation between the Moore-Penrose
and commuting reciprocal inverses. SIAM J. Appl. Math., 24:44-49,
1973. BibTeX entry |
| [1198] | V. Lovass-Nagy and D. L. Powers. A note on the ``Y-inverse''
of a matrix. Internat. J. Control (1), 18:1113-1115, 1973. BibTeX entry |
| [1199] | V. Lovass-Nagy and D. L. Powers. On a relation among generalized
inverses, with application to the Moore-Penrose inverse of certain Toeplitz
matrices. Indust. Math., 24:67-76, 1974. BibTeX entry |
| [1200] | V. Lovass-Nagy and D. L. Powers. Matrix generalized inverses in the
handling of control problems containing input derivatives. Internat.
J. Systems Sci., 6:693-696, 1975. BibTeX entry |
| [1201] | V. Lovass-Nagy and D. L. Powers. On rectangular systems of differential
equations and their application to circuit theory. J. Franklin Inst.
, 299(6):399-407, 1975. BibTeX entry |
| [1202] | Per-Olov Löwdin. Studies in perturbation theory. IV. Solution
of eigenvalue problem by projection operator formalism. J. Mathematical
Phys., 3:969-982, 1962. BibTeX entry |
| [1203] | J. M. Lowerre. Some relationships between blu
es, wises and sls
es. J. Amer. Statist. Assoc., 69:223-225, 1974. (see
[81]
). BibTeX entry |
| [1204] | J. M. Lowerre. Some simplifying results on BLUEs. J. Amer. Statist.
Assoc., 72(358):433-437, 1977. BibTeX entry |
| [1205] | K. Löwner. Über monotone Matrixfunktionen. Math. Z.
, 38:177-216, 1934. BibTeX entry |
| [1206] | Senquan Lu and Guorong Wang. A parallel algorithm for computing the
minimum n-norm m-least squares solution to an inconsistent
system of linear equations (chinese). J. Shanghai Teachers University
, 22(2):1-7, 1993. BibTeX entry |
| [1207] | Shi Jie Lu. The range and pseudo-inverse of a product. Tohoku
Math. J. (2), 39(1):89-94, 1987. BibTeX entry |
| [1208] | Shi Jie Lu. An application of pseudo-inverses-the analytic characteristic
of T-regular points for closed operators. Tohoku Math. J. (2)
, 40(3):331-341, 1988. BibTeX entry |
| [1209] | G. R. Luecke. A numerical procedure for computing the Moore-Penrose
inverse. Numer. Math., 32(2):129-137, 1979. BibTeX entry |
| [1210] | G. Lukács. The generalized inverse matrix and the surface-surface
intersection problem. In Theory and Practice of Geometric Modeling
(Blaubeuren, 1988), pages 167-185. Springer, Berlin, 1989. BibTeX entry |
| [1211] | I. I. Lyashko, V. Yu. Kudrinski\i, and V. S. Ostapchuk. A method
for determining the generalized normal solution of a system of linear algebraic
equations. Dokl. Akad. Nauk Ukrain. SSR Ser. A, (7):16-20, 1985. BibTeX entry |
| [1212] | C. C. MacDuffee. The Theory of Matrices. Chelsea, New York,
1956. BibTeX entry |
| [1213] | Jitka Machalová. Chipman pseudoinverse of matrix, its computation
and application in spline theory. Acta Univ. Palack. Olomuc. Fac.
Rerum Natur. Math., 39:143-157, 2000. BibTeX entry |
| [1214] | G. Maeß. A projection method solving general linear algebraic
equations. Rostock. Math. Kolloq., 12:77-85, 1979. (extension
of results of [1799]
). BibTeX entry |
| [1215] | G. Maeß. Iterative solution of rectangular systems of linear
algebraic equations. In Computational Mathematics (Warsaw, 1980)
, pages 527-533, Warsaw, 1984. PWN. BibTeX entry |
| [1216] | G. Maeß and W. Peters. Lösung inkonsistenter linearer
Gleichungssysteme und Bestimmung einer Pseudoinversen für rechteckige
Matrizen durch Spaltenapproximation. Z. Angew. Math. Mech., 58(4):233-237,
1978. BibTeX entry |
| [1217] | J. R. Magnus and H. Neudecker. Matrix Differential Calculus with
Applications in Statistics and Econometrics. John Wiley & Sons
Ltd., Chichester, 1999. (revised reprint of the 1988 original). BibTeX entry |
| [1218] | P. J. Maher. Some operator inequalities concerning generalized inverses.
Illinois J. Math., 34(3):503-514, 1990. BibTeX entry |
| [1219] | P. J. Maher. Some norm inequalities concerning generalized inverses.
Linear Algebra and its Applications, 174:99-110, 1992. BibTeX entry |
| [1220] | T. Mäkeläinen. Projections and generalized inverses in
the general linear model. Soc. Sci. Fenn. Comment. Phys.-Math.,
38:13-25, 1970. BibTeX entry |
| [1221] | O. L. Mangasarian. Characterizations of real matrices of monotone
kind. SIAM Rev., 10:439-441, 1968. BibTeX entry |
| [1222] | R. K. Manherz. New energy theorems in Fourier transform theory.
Proc. IEEE, 57:826-827, 1969. BibTeX entry |
| [1223] | R. K. Manherz and S. L. Hakimi. The generalized inverse in network
analysis and quadratic error-minimization problems. IEEE Trans. Circuit
Theory, CT-16:559-562, 1969. BibTeX entry |
| [1224] | M. Marcus. Finite Dimensional Multilinear Algebra, Part 1.
Marcel Dekker, New York, 1973. BibTeX entry |
| [1225] | M. Marcus. Finite Dimensional Multilinear Algebra, Part 2.
Marcel Dekker, New York, 1975. BibTeX entry |
| [1226] | M. Marcus. A unified exposition of some classical matrix theorems.
Linear and Multilinear Algebra, 25:137-147, 1989. BibTeX entry |
| [1227] | M. Marcus and H. Minc. A Survey of Matrix Theory and Matrix Inequalities
. Allyn & Bacon, Boston, Mass., 1964. BibTeX entry |
| [1228] | T. L. Markham. An application of theorems of Schur and Albert.
Proc. Amer. Math. Soc., 59(2):205-210, 1976. BibTeX entry |
| [1229] | A. Markiewicz. Characterization of general ridge estimators.
Statist. Probab. Lett., 27(2):145-148, 1996. BibTeX entry |
| [1230] | A. Markiewicz. Simultaneous polar decomposition of rectangular complex
matrices. Linear Algebra and its Applications, 289(1-3):279-284,
1999. (application of [862]
). BibTeX entry |
| [1231] | M. D. Marquardt. Generalized inverses, ridge regression, biased linear
estimation, and nonlinear regression. Technometrics, 12:591-613,
1970. BibTeX entry |
| [1232] | G. Marsaglia. Conditional means and variances of normal variables
with singular convariance matrix. J. Amer. Statist. Assoc., 58:1203-1204,
1964. BibTeX entry |
| [1233] | G. Marsaglia and G. P. H. Styan. Equalities and inequalities for
ranks of matrices. Linear and Multilinear Algebra, 2:269-292, 1974/75. BibTeX entry |
| [1234] | J. T. Marti. An algorithm for computing minimum norm solutions of
Fredholm integral equations of the first kind. SIAM J. Numer. Anal.
, 15(6):1071-1076, 1978. (see [891]
). BibTeX entry |
| [1235] | R. S. Martin, G. Peters, and J. H. Wilkinson. Iterative refinement
of the solution of a positive definite system of equations. Numer.
Math., 8:203-216, 1966. (republished, pp. 31-44 in
[2058]
). BibTeX entry |
| [1236] | J. M. Martínez. A bound for the Moore-Penrose pseudoinverse
of a matrix. Comment. Math. Univ. Carolin., 20(2):357-360, 1979. BibTeX entry |
| [1237] | E. Martínez-Torres. Formulation of the vibrational theory
in terms of redundant internal coordinates. Journal of Molecular Structure
, 520:53-61, 2000. BibTeX entry |
| [1238] | Mathematical Genealogy Project. http:\\hcoonce.math.mankato.msus.edu/index.html
. BibTeX entry |
| [1239] | T. Mathew and S. K. Mitra. Shorted operators and the identification
problem-the real case. IEEE Trans. Circuits and Systems, 31(3):299-300,
1984. BibTeX entry |
| [1240] | J. C. Maxwell. Treatise of Electricity and Magnetism, volume
I. Oxford University Press, Oxford, 3rd edition, 1892. BibTeX entry |
| [1241] | D. Q. Mayne. An algorithm for the calculation of the pseudo-inverse
of a singular matrix. Comput. J., 9:312-317, 1966. BibTeX entry |
| [1242] | D. Q. Mayne. On the calculation of pseudoinverses. IEEE Trans.
Automatic Control, AC-14:204-205, 1969. BibTeX entry |
| [1243] | M. Mbekhta. On the generalized resolvent in Banach spaces. J.
Math. Anal. Appl., 189(2):362-377, 1995. BibTeX entry |
| [1244] | R. V. Mayorga, A. K. C. Wong, and N. Milano. A fast procedure for
manipulator inverse kinematics evaluation and pseudoinverse robustness.
IEEE Trans. Systems Man Cybernet., 22(4):790-798, 1992. BibTeX entry |
| [1245] | N. H. McCoy. Generalized regular rings. Bull. Amer. Math. Soc.
, 45:175-178, 1939. BibTeX entry |
| [1246] | G. C. McDonald. Some algebraic properties of ridge coefficients.
J. Roy. Statist. Soc. B, 42(1):31-34, 1980. BibTeX entry |
| [1247] | J. S. McMath and S. E. Sims. Mean value theorems for a matrix valued
derivative. Linear and Multilinear Algebra, 9(4):255-261, 1980/81. BibTeX entry |
| [1248] | J. S. McMath, S. E. Sims, and C. R. Hallum. On the properties of
a matrix valued derivative utilizing the Moore-Penrose inverse. Linear
Algebra and its Applications, 18(3):281-291, 1977. (see
[1247]
). BibTeX entry |
| [1249] | J. S. McMath, S. E. Sims, and C. R. Hallum. A comparison of various
derivatives for matrix-valued functions. Comput. Math. Appl., 6(2):161-166,
1980. BibTeX entry |
| [1250] | A. Meenakshi. On integral EPr matrices. Period.
Math. Hungar., 14(3-4):229-234, 1983. BibTeX entry |
| [1251] | A. Meenakshi and N. Anandam. Polynomial generalized inverses of a
partitioned polynomial matrix. J. Indian Math. Soc. (N.S.), 58(1-4):11-18,
1992. BibTeX entry |
| [1252] | M. Meicler. Chebyshev solution of an inconsistent system of n
+1 linear equations in n unknowns in terms of its least squares
solution. SIAM Rev., 10:373-375, 1968. BibTeX entry |
| [1253] | M. Meicler. A steepest ascent method for the Chebyshev problem.
Math. Comp., 23:813-817, 1969. BibTeX entry |
| [1254] | E. Meister and F. -O. Speck. The Moore-Penrose inverse of Wiener-Hopf
operators on the half axis and the quarter plane. J. Integral Equations
, 9(1):45-61, 1985. BibTeX entry |
| [1255] | V. I. Melesko. Statistical recurrent estimation based on pseudoinverse
operators. Avtomat. i Telemeh., (8):101-110, 1976. (English translation
Automat. Remote Control 37(1976), no. 8, part 2, 1227-1235
(1977). BibTeX entry |
| [1256] | V. I. Melesko. Pseudoinverse operators in Banach spaces. Ukrain.
Mat. Z., 29(6):738-749, 851, 1977. English translation: Ukrainian
Math. J. 29 (1977), no. 6, 545-553. BibTeX entry |
| [1257] | V. I. Melesko. A pseudo-inversion of closed operators that is stable
under perturbations. Z. Vycisl. Mat. i Mat. Fiz., 17(5):1132-1143,
1332, 1977. BibTeX entry |
| [1258] | V. I. Melesko. Pseudoinverse operators, and the recursive calculation
of pseudosolutions in Hilbert spaces. Sibirsk. Mat. Z., 19(1):108-121,
238, 1978. (generalization of Greville's method to Hilbert space, see
[706]
. English translation: Siberian Math. J. 19 (1978), no. 1,
75-85). BibTeX entry |
| [1259] | V. I. Melesko. Perturbations of unbounded closed pseudoinverse operators.
Differentsial' nye Uravneniya, 15(4):681-694, 765, 1979. English
translation: Differential Equations 15 (1979), no. 4, 477-487 (1980). BibTeX entry |
| [1260] | V. I. Melesko. An investigation of stable L-pseudo-inverses
of unbounded closed operators by the regularization method. Differentsial'
nye Uravneniya, 15(5):921-935, 958-959, 1979. English translation:
Differential Equations 15 (1979), no. 5, 653-664. BibTeX entry |
| [1261] | V. I. Melesko. Properties of pseudo-inverse operators in Banach spaces.
Dokl. Akad. Nauk SSSR, 249(5):1055-1059, 1979. BibTeX entry |
| [1262] | V. I. Melesko. Filtering and identification of stochastic control
systems using pseudoinverses. Kibernetika (Kiev), (5):130-140,
1980. BibTeX entry |
| [1263] | V. I. Melesko. Perturbed iteration methods for determining L
generalized solutions of nonlinear operator equations. Differentsial'
nye Uravneniya, 17(3):541-557, 574-575, 1981. (English translation:
Differential Equations 17 (1981), no. 3, 377-390). BibTeX entry |
| [1264] | V. I. Melesko. Algorithms of pseudoinverse operators for calculating
generalized solutions of nonlinear equations. I. Avtomat. Sistemy
Upravleniya i Pribory Avtomat., (59):45-51, ii-iii, 1981. (Newton
method, see [1265]
). BibTeX entry |
| [1265] | V. I. Melesko. Algorithms of pseudoinverse operators for calculating
generalized solutions of nonlinear equations. II. Avtomat. Sistemy
Upravleniya i Pribory Avtomat., (60):20-27, 1981. (Newton method). BibTeX entry |
| [1266] | V. I. Melesko. Perturbation-resistant algorithms for pseudoinversion
of rectangular matrices using the Lagrange transform. In Mathematical
Methods of Cybernetics, pages 24-37. Akad. Nauk Ukrain. SSR Inst. Kibernet.,
Kiev, 1982. BibTeX entry |
| [1267] | V. I. Melesko. Regularized nonorthogonal factorizations and pseudoinversions
of perturbed matrices. Zh. Vychisl. Mat. i Mat. Fiz., 26(4):485-498,
638, 1986. BibTeX entry |
| [1268] | V. I. Melesko. Accelerated regularized methods for calculating solutions
of nonlinear nonregular equations. Dokl. Akad. Nauk SSSR, 311(2):282-287,
1990. (English translation: Soviet Math. Dokl. 41 (1990), no. 2, 246-251
(1991)). BibTeX entry |
| [1269] | V. I. Melesko and V. M. Zadachin. Factorizations and pseudo-inversions
of singular perturbed matrices with nonfixed signs. Izv. Vyssh. Uchebn.
Zaved. Mat., (11):42-50, 88, 1987. (English translation: Soviet
Math. (Iz. VUZ) 31 (1987), no. 11, 53-62). BibTeX entry |
| [1270] | G. Merz. Über die Interpolationsaufgabe bei natürlichen
Polynom-Splines mit äquidistanten Knoten. J. Approximation Theory
, 10:151-158, 1974. BibTeX entry |
| [1271] | F. T. Metcalf. A Bessel-Schwarz inequality for Gramians and related
bounds for determinants. Ann. Mat. Pura Appl. (4), 68:201-232,
1965. BibTeX entry |
| [1272] | C. D. Meyer, Jr. On ranks of pseudoinverses. SIAM Rev.,
11:382-385, 1969. BibTeX entry |
| [1273] | C. D. Meyer, Jr. On the construction of solutions to the matrix equations
AX=A and YA=A. SIAM
Rev., 11:612-615, 1969. BibTeX entry |
| [1274] | C. D. Meyer, Jr. Generalized inverses of triangular matrices.
SIAM J. Appl. Math., 18:401-406, 1970. BibTeX entry |
| [1275] | C. D. Meyer, Jr. Some remarks on EPr matrices, and
generalized inverses. Linear Algebra and its Applications, 3:275-278,
1970. BibTeX entry |
| [1276] | C. D. Meyer, Jr. Generalized inverses of block triangular matrices.
SIAM J. Appl. Math., 19:741-750, 1970. BibTeX entry |
| [1277] | C. D. Meyer, Jr. Representations for (1)- and (1,2)-inverses for
partitioned matrices. Linear Algebra and its Applications, 4:221-232,
1971. BibTeX entry |
| [1278] | C. D. Meyer, Jr. The Moore-Penrose inverse of a bordered matrix.
Linear Algebra and its Applications, 5:375-382, 1972. BibTeX entry |
| [1279] | C. D. Meyer, Jr. Generalized inversion of modified matrices.
SIAM J. Appl. Math., 24:315-323, 1973. BibTeX entry |
| [1280] | C. D. Meyer, Jr. Generalized inverses and ranks of block matrices.
SIAM J. Appl. Math., 25:597-602, 1973. BibTeX entry |
| [1281] | C. D. Meyer, Jr. Limits and the index of a square matrix. SIAM
J. Appl. Math., 26:469-478, 1974. (see [1636]
). BibTeX entry |
| [1282] | C. D. Meyer, Jr. The role of the group generalized inverse in the
theory of finite Markov chains. SIAM Rev., 17:443-464, 1975. BibTeX entry |
| [1283] | C. D. Meyer, Jr. Analysis of finite Markov chains by group inversion
techniques. In Campbell [318]
, pages 50-81. BibTeX entry |
| [1284] | C. D. Meyer, Jr. The character of a finite Markov chain. In
Linear Algebra, Markov Chains, and Queueing Models (Minneapolis, MN, 1992)
, pages 47-58. Springer, New York, 1993. BibTeX entry |
| [1285] | C. D. Meyer, Jr. Matrix Analysis and Applied Linear Algebra
. Society for Industrial and Applied Mathematics (SIAM), Philadelphia,
PA, 2000. BibTeX entry |
| [1286] | C. D. Meyer, Jr. and R. J. Painter. Note on a least squares inverse
for a matrix. J. Assoc. Comput. Mach., 17:110-112, 1970. BibTeX entry |
| [1287] | C. D. Meyer, Jr. and R. J. Plemmons. Convergent powers of a matrix
with applications to iterative methods for singular linear systems.
SIAM J. Numer. Anal., 14(4):699-705, 1977. BibTeX entry |
| [1288] | C. D. Meyer, Jr. and N. J. Rose. The index and the Drazin inverse
of block triangular matrices. SIAM J. Appl. Math., 33(1):1-7, 1977. BibTeX entry |
| [1289] | C. D. Meyer, Jr. and J. M. Shoaf. Updating finite Markov chains by
using techniques of group matrix inversion. J. Statist. Comput. Simulation
, 11(3-4):163-181, 1980. BibTeX entry |
| [1290] | C. D. Meyer, Jr. and M. W. Stadelmaier. Singular M-matrices
and inverse positivity. Linear Algebra and its Applications, 22:139-156,
1978. BibTeX entry |
| [1291] | C. D. Meyer, Jr. and G. W. Stewart. Derivatives and perturbations
of eigenvectors. SIAM J. Numer. Anal., 25(3):679-691, 1988. BibTeX entry |
| [1292] | Jian Ming Miao. The weighted Moore-Penrose inverse of a rank-one
modified matrix (chinese). J. Shanghai Teachers University, 17(3):21-26,
1988. BibTeX entry |
| [1293] | Jian Ming Miao. Representations for the weighted Moore-Penrose inverse
of a partitioned matrix. J. Comput. Math., 7(4):321-323, 1989. BibTeX entry |
| [1294] | Jian Ming Miao. The Moore-Penrose inverse of a rank-r modified
matrix. Numer. Math. J. Chinese Univ., 11(4):355-361, 1989. BibTeX entry |
| [1295] | Jian Ming Miao. Some results on the Drazin inverses for partitioned
matrices (Chinese). J. Shanghai Teachers University, 18(2):25-31,
1989. BibTeX entry |
| [1296] | Jian Ming Miao. Representations for the weighted Moore-Penrose inverse
of sums of matrices (Chinese). Comm. Appl. Math. and Comput.,
3(2):83-86, 1989. BibTeX entry |
| [1297] | Jian Ming Miao. The Drazin inverse of Hessenberg matrices. J.
Comput. Math., 8(1):23-29, 1990. BibTeX entry |
| [1298] | Jian Ming Miao. General expressions for the Moore-Penrose inverse
of a 2× 2 block matrix. Linear Algebra and its Applications
, 151:1-15, 1991. BibTeX entry |
| [1299] | Jian Ming Miao. Reflexive generalized inverses and their minors.
Linear and Multilinear Algebra, 35(2):153-163, 1993. BibTeX entry |
| [1300] | Jian Ming Miao and A. Ben-Israel. On principal angles between subspaces
in R n. Linear Algebra and its Applications, 171:81-98,
1992. BibTeX entry |
| [1301] | Jian Ming Miao and A. Ben-Israel. Minors of the Moore-Penrose inverse.
Linear Algebra and its Applications, 195:191-207, 1993. BibTeX entry |
| [1302] | Jian Ming Miao and A. Ben-Israel. On l p-approximate
solutions of linear equations. Linear Algebra and its Applications
, 199:305-327, 1994. BibTeX entry |
| [1303] | Jian Ming Miao and A. Ben-Israel. The geometry of basic, approximate,
and minimum-norm solutions of linear equations. Linear Algebra and
its Applications, 216:25-41, 1995. BibTeX entry |
| [1304] | Jian Ming Miao and A. Ben-Israel. Product cosines of angles between
subspaces. Linear Algebra and its Applications, 237/238:71-81, 1996. BibTeX entry |
| [1305] | Jian Ming Miao and D. W. Robinson. Group and Moore-Penrose inverses
of regular morphisms with kernel and cokernel. Linear Algebra and
its Applications, 110:263-270, 1988. BibTeX entry |
| [1306] | C. Miehe and J. Schröder. Comparative study of stress update
algorithms for rate-independent and rate-dependent crystal plasticity.
Internat. J. Numer. Methods Engrg., 50:273-298, 2001. BibTeX entry |
| [1307] | L. Mihályffy. A note on the matrix inversion by the partitioning
technique. Studia Sci. Math. Hungar., 5:127-135, 1970. BibTeX entry |
| [1308] | L. Mihályffy. An alternative representation of the generalized
inverse of partitioned matrices. Linear Algebra and its Applications
, 4:95-100, 1971. BibTeX entry |
| [1309] | A. J. Miller and B. D. Cornuelle. Forecasts from fits of frontal
fluctuations. Dynamics of Atmospheres and Oceans, 29(2-4):305-333,
1999. BibTeX entry |
| [1310] | G. A. Milliken and F. Akdeniz. A theorem on the difference of the
generalized inverses of two nonnegative matrices. Comm. Statist.-Theory
Methods, A6(1):73-79, 1977. BibTeX entry |
| [1311] | R. D. Milne. An oblique matrix pseudoinverse. SIAM J. Appl.
Math., 16:931-944, 1968. (see [1977]
). BibTeX entry |
| [1312] | H. W. Milnes, J. Amburgey, T. O. Lewis, and T. L. Boullion. Spectral
eigenvalue property of A+ for rectangular matrices. In Boullion
and Odell [255]
, pages 98-113. BibTeX entry |
| [1313] | N. Minamide and K. Nakamura. Minimum error control problem in banach
space. Research Report of Automatic Control Lab 16, Nagoya University,
Nagoya, Japan, 1969. BibTeX entry |
| [1314] | N. Minamide and K. Nakamura. A restricted pseudoinverse and its applications
to constrained minima. SIAM J. Appl. Math., 19:167-177, 1970. BibTeX entry |
| [1315] | L. Mirsky. Symmetric gauge functions and unitarily invariant norms.
Quart. J. Math. Oxford, 11:50-59, 1960. BibTeX entry |
| [1316] | S. K. Mitra. On a generalized inverse of a matrix and applications.
Sankhya Ser. A, 30:107-114, 1968. BibTeX entry |
| [1317] | S. K. Mitra. A new class of g-inverse of square matrices. Sankhya
Ser. A, 30:323-330, 1968. BibTeX entry |
| [1318] | S. K. Mitra. Fixed rank solutions of linear matrix equations.
Sankhya Ser. A, 35:387-392, 1972. BibTeX entry |
| [1319] | S. K. Mitra. Common solutions to a pair of linear matrix equations
A1 XB1=C1,
A2 XB2=C2. Proceedings
of the Cambridge Philosophical Society, 74:213-216, 1973. BibTeX entry |
| [1320] | S. K. Mitra. Shorted operators and the identification problem.
IEEE Trans. Circuits and Systems, 29(8):581-583, 1982. BibTeX entry |
| [1321] | S. K. Mitra. Simultaneous diagonalization of rectangular matrices.
Linear Algebra and its Applications, 47:139-150, 1982. BibTeX entry |
| [1322] | S. K. Mitra. The minus partial order and the shorted matrix.
Linear Algebra and its Applications, 83:1-27, 1986. BibTeX entry |
| [1323] | S. K. Mitra. On group inverses and the sharp order. Linear Algebra
and its Applications, 92:17-37, 1987. BibTeX entry |
| [1324] | S. K. Mitra. Block independence in generalized inverses: A coordinate
free look. In Statistical Data Analysis and Inference (Y. Dodge, ed.)
, pages 429-443. North Holland, Amsterdam, 1989. BibTeX entry |
| [1325] | S. K. Mitra. Shorted matrices in star and related orderings.
Circuits Systems Signal Process., 9(2):197-212, 1990. BibTeX entry |
| [1326] | S. K. Mitra. Matrix partial order through generalized inverses: unified
theory. Linear Algebra and its Applications, 148:237-263, 1991. BibTeX entry |
| [1327] | S. K. Mitra. Separation theorems. Linear Algebra and its Applications
, 208/209:239-256, 1994. BibTeX entry |
| [1328] | S. K. Mitra. Erratum: ``The nonunique shorted matrix'' [Linear Algebra
Appl. 237/238 (1996), 41-70; MR 97a:15012] by Mitra and K. M.
Prasad. Linear Algebra and its Applications, 260:323, 1997. BibTeX entry |
| [1329] | S. K. Mitra. Diagrammatic presentation of inner and outer inverses:
S-diagrams. Linear Algebra and its Applications, 287(1-3):271-288,
1999. BibTeX entry |
| [1330] | S. K. Mitra and P. Bhimasankaram. Generalized inverses of partitioned
matrices and recalculation of least squares estimates for data or model
changes. Sankhya Ser. A, 33:395-410, 1971. BibTeX entry |
| [1331] | S. K. Mitra and R. E. Hartwig. Partial orders based on outer inverses.
Linear Algebra and its Applications, 176:3-20, 1992. BibTeX entry |
| [1332] | S. K. Mitra and P. L. Odell. On parallel summability of matrices.
Linear Algebra and its Applications, 74:239-255, 1986. BibTeX entry |
| [1333] | S. K. Mitra and K. M. Prasad. The nonunique shorted matrix.
Linear Algebra and its Applications, 237/238:41-70, 1996. (erratum
in [1328]
). BibTeX entry |
| [1334] | S. K. Mitra and K. M. Prasad. The nonunique parallel sum. Linear
Algebra and its Applications, 259:77-99, 1997. BibTeX entry |
| [1335] | S. K. Mitra and M. L. Puri. Shorted operators and generalized inverses
of matrices. Linear Algebra and its Applications, 25:45-56, 1979. BibTeX entry |
| [1336] | S. K. Mitra and M. L. Puri. Shorted matrices-an extended concept
and some applications. Linear Algebra and its Applications, 42:57-79,
1982. BibTeX entry |
| [1337] | S. K. Mitra and M. L. Puri. The fundamental bordered matrix of linear
estimation and the Duffin-Morley general linear electromechanical systems.
Applicable Anal., 14(4):241-258, 1983. BibTeX entry |
| [1338] | S. K. Mitra and C. R. Rao. Some results in estimation and tests of
linear hypotheses under the Gauss-Markov model. Sankhya Ser. A
, 30:281-290, 1968. BibTeX entry |
| [1339] | S. K. Mitra and C. R. Rao. Conditions for optimality and validity
of simple least squares theory. Ann. Math. Statist., 40:1617-1624,
1969. BibTeX entry |
| [1340] | S. K. Mitra and C. R. Rao. Projections under seminorms and generalized
Moore Penrose inverses. Linear Algebra and its Applications, 9:155-167,
1974. BibTeX entry |
| [1341] | V. J. Mizel and M. M. Rao. Nonsymmetric projections in Hilbert space.
Pacific J. Math., 12:343-357, 1962. BibTeX entry |
| [1342] | S. R. Mohan, M. Neumann, and K. G. Ramamurthy. Nonnegativity of principal
minors of generalized inverses of m-matrices. Linear Algebra
and its Applications, 58:247-259, 1984. BibTeX entry |
| [1343] | S. Mohideen and V. Cherkassky. On recursive calculation of the generalized
inverse of a matrix. ACM Trans. Math. Software, 17(1):130-147, 1991. BibTeX entry |
| [1344] | A. Mohsen and J. Stoer. A variable metric method for approximating
generalized inverses of matrices. ZAMM Z. Angew. Math. Mech.,
81(7):435-446, 2001. BibTeX entry |
| [1345] | I. N. Molcanov and E. F. Galba. Generalized difference Green functions
and elements of pseudoinverse matrices. In Questions on Numerical
Mathematics, pages 27-33, 40. Akad. Nauk Ukrain. SSR Inst. Kibernet.,
Kiev, 1980. BibTeX entry |
| [1346] | I. N. Molcanov and E. F. Galba. Difference methods for elliptic partial
differential equations with nonunique solutions. SIAM J. Numer. Anal.
, 19(3):531-547, 1982. BibTeX entry |
| [1347] | I. N. Molcanov and E. F. Galba. A weighted pseudoinverse for complex
matrices. Ukrain. Mat. Zh., 35(1):53-57, 134, 1983. BibTeX entry |
| [1348] | I. N. Molcanov and E. F. Galba. Weighted pseudo-inversion of matrices
with positive-definite weights. Dokl. Akad. Nauk Ukrain. SSR Ser. A
, (7):15-17, 85, 1989. BibTeX entry |
| [1349] | C. B. Moler. Iterative refinement in floating point. J. Assoc.
Comput. Mach., 14:316-321, 1967. BibTeX entry |
| [1350] | C. B. Moler and C. F. Van Loan. Nineteen dubious ways to compute
the exponential of a matrix. SIAM Rev., 20:801-836, 1978. BibTeX entry |
| [1351] | W. Mönch. Monotone Einschliessung der Moore-Penrose Pseudoinversen
einer Matrix. Z. Angew. Math. Mech., 58(2):67-74, 1978. BibTeX entry |
| [1352] | W. Mönch. Iterative refinement of approximations to a generalized
inverse of a matrix. Computing, 28(1):79-87, 1982. BibTeX entry |
| [1353] | B. Mond. Generalized inverse extensions of matrix inequalities.
Linear Algebra and its Applications, 2:393-399, 1969. BibTeX entry |
| [1354] | B. Mond and J. E. Pecaric. Inequalities with weights for powers of
generalised inverses. Bull. Austral. Math. Soc., 48(1):7-12, 1993. BibTeX entry |
| [1355] | B. Mond and J. E. Pecaric. Inequalities with weights for powers of
generalized inverses. II. Linear Algebra and its Applications, 210:265-272,
1994. BibTeX entry |
| [1356] | B. Mond and J. E. Pecaric. On matrix convexity of the Moore-Penrose
inverse. Internat. J. Math. Math. Sci., 19(4):707-710, 1996. BibTeX entry |
| [1357] | B. Mond and J. E. Pecaric. Hadamard products and generalized inverses.
Austral. Math. Soc. Gaz., 25(4):194-197, 1998. BibTeX entry |
| [1358] | E. H. Moore. On a form of general analysis with applications to linear
differential equations and integral equations. In Atti del IV Congresso
Internazionale dei Matematici (Rome 1908). Vol 2, pages 98-114. Roma,
1909. BibTeX entry |
| [1359] | E. H. Moore. Introduction to a Form of General Analysis. In
The New Haven Mathematical Colloquium, pages 1-150. Yale University
Press, New Haven, CT, 1910. (see review in [210]
). BibTeX entry |
| [1360] | E. H. Moore. On the foundations of the theory of linear integral
equations. Trans. Amer. Math. Soc., 18:334-362, 1912. BibTeX entry |
| [1361] | E. H. Moore. On the fundamental functional operation of a general
theory of linear integral equations. In Proceedings of the 5th International
Congress of Mathematicians, pages 230-255. Cambridge, 1912. BibTeX entry |
| [1362] | E. H. Moore. Definition of limit in general integral analysis.
Proc. Nat. Acad. Sci., 1:628, 1915. BibTeX entry |
| [1363] | E. H. Moore. On properly positive Hermitian matrices. Bull.
Amer. Math. Soc., 23:59, 1916. BibTeX entry |
| [1364] | E. H. Moore. On the reciprocal of the general algebraic matrix.
Bull. Amer. Math. Soc., 26:394-395, 1920. (Abstract). BibTeX entry |
| [1365] | E. H. Moore and R. W. Barnard. General Analysis. Memoirs
of the American Philosophical Society, I. American Philosophical Society,
Philadelphia, Pennsylvania, 1935. (see specially Part 1, pp. 197-209). BibTeX entry |
| [1366] | E. H. Moore and H. L. Smith. A general theory of limits. Amer.
J. Math., 44:102-121, 1922. BibTeX entry |
| [1367] | R. H. Moore and M. Z. Nashed. Approximations of generalized inverses
of linear operators in Banach spaces. In Approximation Theory (Proc.
Internat. Sympos., Univ. Texas, Austin, TX, 1973), pages 425-428. Academic
Press, New York, 1973. BibTeX entry |
| [1368] | R. H. Moore and M. Z. Nashed. Approximations to generalized inverses
of linear operators. SIAM J. Appl. Math., 27:1-16, 1974. BibTeX entry |
| [1369] | C. F. Moppert. On the Gram determinant. Quart. J. Math. Oxford
Ser. (2), 10:161-164, 1959. BibTeX entry |
| [1370] | T. D. Morley. Parallel summation, Maxwell's principle and the infimum
of projections. J. Math. Anal. Appl., 70(1):33-41, 1979. BibTeX entry |
| [1371] | T. D. Morley. A Gauss-Markov theorem for infinite-dimensional regression
models with possibly singular covariance. SIAM J. Appl. Math.,
37(2):257-260, 1979. BibTeX entry |
| [1372] | T. D. Morley. An alternative approach to the parallel sum. Adv.
in Appl. Math., 10(3):358-369, 1989. BibTeX entry |
| [1373] | V. A. Morozov. The principle of disparity in solving operator equations
by the method of regularization. Z. Vycisl. Mat. i Mat. Fiz.,
8:295-309, 1968. BibTeX entry |
| [1374] | V. A. Morozov. Pseudosolutions. Z. Vycisl. Mat. i Mat. Fiz.
, 9:1387-1391, 1969. BibTeX entry |
| [1375] | V. A. Morozov. The optimal regularization of operator equations.
Z. Vycisl. Mat. i Mat. Fiz., 10:818-829, 1970. BibTeX entry |
| [1376] | V. A. Morozov. An effective numerical algorithm for constructing
pseudosolutions. Z. Vycisl. Mat. i Mat. Fiz., 11:260-262, 1971. BibTeX entry |
| [1377] | V. A. Morozov. Methods for Solving Incorrectly Posed Problems
. Springer-Verlag, New York, 1984. Translated from the Russian by A.
B. Aries, Translation edited by Z. Nashed. BibTeX entry |
| [1378] | G. L. Morris and P. L. Odell. Common solutions for n matrix
equations with applications. J. Assoc. Comput. Mach., 15:272-274,
1968. BibTeX entry |
| [1379] | G. L. Morris and P. L. Odell. A characterization for generalized
inverses of matrices. SIAM Rev., 10:208-211, 1968. BibTeX entry |
| [1380] | G. D. Mostow and J. H. Sampson. Linear Algebra. McGraw-Hill,
New York, 1969. BibTeX entry |
| [1381] | G. D. Mostow, J. H. Sampson, and J. -P. Meyer. Fundamental Structures
of Algebra. McGraw-Hill, New York, 1963. BibTeX entry |
| [1382] | L. Moura and R. Kitney. A direct method for least-squares circle
fitting. Comput. Phys. Comm., 64(1):57-63, 1991. (see
[1437]
). BibTeX entry |
| [1383] | C. Müller. Spherical Harmonics. Lecture Notes in Mathematics,
No. 17. Springer-Verlag, New York, 1966. BibTeX entry |
| [1384] | W. D. Munn. Pseudoinverses in semigroups. Proc. Cambridge Phil.
Soc., 57:247-250, 1961. BibTeX entry |
| [1385] | W. D. Munn. Moore-Penrose inversion in complex contracted inverse
semigroup algebras. J. Austral. Math. Soc. Ser. A, 66(3):297-302,
1999. BibTeX entry |
| [1386] | W. D. Munn and R. Penrose. A note on inverse semigroups. Proceedings
of the Cambridge Philosophical Society, 51:396-399, 1955. BibTeX entry |
| [1387] | K. Murakami and T. Aibara. An improvement on the Moore-Penrose generalized
inverse associative memory. IEEE Trans. Systems Man Cybernet.,
17(4):699-707, 1987. BibTeX entry |
| [1388] | F. D. Murnaghan and A. Wintner. A canonical form for real matrices
under orthogonal transformation. Proc. Nat. Acad. Sci. U.S.A., 17:417-420,
1931. BibTeX entry |
| [1389] | F. J. Murray and J. von Neumann. On rings of operators. Ann.
of Math., 37:116-229, 1936. BibTeX entry |
| [1390] | K. V. V. Murthy and V. Ramachandran. On the ranks of certain matrices.
Matrix Tensor Quart., 31(3):67-69, 1980/81. BibTeX entry |
| [1391] | K. N. Murty and P. V. S. Lakshmi. On two-point boundary value problems.
J. Math. Anal. Appl., 153(1):217-225, 1990. BibTeX entry |
| [1392] | M. S. N. Murty and D. R. K. S. Rao. Application of generalized inverses
to two-point boundary value problems. Bull. Inst. Math. Acad. Sinica
, 19(3):271-278, 1991. BibTeX entry |
| [1393] | M. S. N. Murty and B. V. Appa Rao. Application of Moore-Penrose inverse
to three point boundary value problems. Ranchi Univ. Math. J.,
29:1-9 (1999), 1998. BibTeX entry |
| [1394] | S. Nakagiri and K. Suzuki. Finite element interval analysis of external
loads identified by displacement input with uncertainty. Computer
Methods in Applied Mechanics and Engineering, 168(1-4):63-72, 1999. BibTeX entry |
| [1395] | K. S. Subramonian Nambooripad. The natural partial order on a regular
semigroup. Proc. Edinburgh Math. Soc. (2), 23(3):249-260, 1980. BibTeX entry |
| [1396] | V. C. Nanda. A generalization of Cayley's theorem. Math. Z.
, 101:331-334, 1967. BibTeX entry |
| [1397] | J. C. Nash. Compact Numerical Methods for Computers. Adam
Hilger Ltd., Bristol, second edition, 1990. BibTeX entry |
| [1398] | J. C. Nash and R. L. C. Wang. Algorithm 645: subroutines for testing
programs that compute the generalized inverse of a matrix. ACM Trans.
Math. Software, 12(3):274-277, 1986. BibTeX entry |
| [1399] | S. G. Nash. Newton-type minimization via the Lánczos method.
SIAM J. Numer. Anal., 21(4):770-788, 1984. BibTeX entry |
| [1400] | M. Z. Nashed. Steepest descent for singular linear operator equations.
SIAM J. Numer. Anal., 7:358-362, 1970. BibTeX entry |
| [1401] | M. Z. Nashed. Generalized inverses, normal solvability, and iteration
for singular operator equations. In Nonlinear Functional Anal. and
Appl. (Proc. Advanced Sem., Math. Res. Center, Univ. of Wisconsin, Madison,
Wis., 1970), pages 311-359. Academic Press, New York, 1971. BibTeX entry |
| [1402] | M. Z. Nashed, editor. Generalized Inverses and Applications (Proc.
Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1973), New
York, 1976. Academic Press. BibTeX entry |
| [1403] | M. Z. Nashed. Generalized inverses in analysis and regularization.
[1402]
, pages 193-244. BibTeX entry |
| [1404] | M. Z. Nashed. Perturbations and approximations for generalized inverses
and linear operator equations. [1402]
, pages 325-396. BibTeX entry |
| [1405] | M. Z. Nashed. On moment-discretization and least-squares solutions
of linear integral equations of the first kind. J. Math. Anal. Appl.
, 53(2):359-366, 1976. BibTeX entry |
| [1406] | M. Z. Nashed. On the perturbation theory for generalized inverse
operators in Banach spaces. In Functional Analysis Methods in Numerical
Analysis (Proc. Special Session, Annual Meeting, Amer. Math. Soc., St.
Louis, MO, 1977), pages 180-195. Springer, Berlin, 1979. BibTeX entry |
| [1407] | M. Z. Nashed. On generalized inverses and operator ranges. In
Functional Analysis and Approximation (Oberwolfach, 1980), pages 85-96.
Birkhäuser, Basel, 1981. BibTeX entry |
| [1408] | M. Z. Nashed and X. Chen. Convergence of Newton-like methods for
singular operator equations using outer inverses. Numer. Math.
, 66:235-257, 1993. BibTeX entry |
| [1409] | M. Z. Nashed and L. B. Rall. Annotated bibliography on generalized
inverses and applications. In Nashed [1402]
, pages 771-1041. BibTeX entry |
| [1410] | M. Z. Nashed and G. F. Votruba. A unified approach to generalized
inverses of linear operators. I. Algebraic, topological and projectional
properties. Bull. Amer. Math. Soc., 80:825-830, 1974. BibTeX entry |
| [1411] | M. Z. Nashed and G. F. Votruba. A unified approach to generalized
inverses of linear operators. II. Extremal and proximal properties.
Bull. Amer. Math. Soc., 80:831-835, 1974. BibTeX entry |
| [1412] | M. Z. Nashed and G. F. Votruba. A unified operator theory of generalized
inverses. In Nashed [1402]
, pages 1-109. BibTeX entry |
| [1413] | M. Z. Nashed and G. Wahba. Generalized inverses in reproducing kernel
spaces: an approach to regularization of linear operator equations.
SIAM J. Math. Anal., 5:974-987, 1974. BibTeX entry |
| [1414] | M. Z. Nashed and G. Wahba. Convergence rates of approximate least
squares solutions of linear integral and operator equations of the first
kind. Math. Comp., 28:69-80, 1974. BibTeX entry |
| [1415] | M. Z. Nashed and Ya Gu Zhao. The Drazin inverse for singular evolution
equations and partial differential operators. In Recent Trends in
Differential Equations, pages 441-456. World Sci. Publishing, River
Edge, NJ, 1992. BibTeX entry |
| [1416] | F. Natterer. The Mathematics of Computerized Tomography.
Wiley, New York, 1986. BibTeX entry |
| [1417] | D. L. Nelson, T. O. Lewis, and T. L. Boullion. A quadratic programming
technique using matrix pseudoinverses. Indust. Math., 21:1-21, 1971. BibTeX entry |
| [1418] | A. Neubauer. Tikhonov-regularization of ill-posed linear operator
equations on closed convex sets. J. Approx. Theory, 53(3):304-320,
1988. BibTeX entry |
| [1419] | A. Neubauer. On converse and saturation results for Tikhonov regularization
of linear ill-posed problems. SIAM J. Numer. Anal., 34(2):517-527,
1997. BibTeX entry |
| [1420] | H. Neudecker. A note on Kronecker matrix products and matrix equation
systems. SIAM J. Appl. Math., 17:603-606, 1969. BibTeX entry |
| [1421] | H. Neudecker. Mathematical properties of the variance of the multinomial
distribution. J. Math. Anal. Appl., 189(3):757-762, 1995. (see
[1805]
). BibTeX entry |
| [1422] | H. Neudecker and Shuangzhe Liu. The density of the Moore-Penrose
inverse of a random matrix. Linear Algebra and its Applications,
237/238:123-126, 1996. BibTeX entry |
| [1423] | A. Neumaier. Hybrid norms and bounds for overdetermined linear systems.
Linear Algebra and its Applications, 216:257-265, 1995. BibTeX entry |
| [1424] | A. Neumaier. Solving ill-conditioned and singular linear systems:
a tutorial on regularization. SIAM Rev., 40(3):636-666 (electronic),
1998. BibTeX entry |
| [1425] | M. Neumann. On the Schur complement and the LU-factorization
of a matrix. Linear and Multilinear Algebra, 9(4):241-254, 1980/81. BibTeX entry |
| [1426] | M. Neumann and R. J. Plemmons. Generalized inverse-positivity and
splittings of M-matrices. Linear Algebra and its Applications, 23:21-35,
1979. BibTeX entry |
| [1427] | M. Neumann, G. D. Poole, and H. -J. Werner. More on generalizations
of matrix monotonicity. Linear Algebra and its Applications, 48:413-435,
1982. BibTeX entry |
| [1428] | M. Neumann and H. -J. Werner. Nonnegative group inverses. Linear
Algebra and its Applications, 151:85-96, 1991. BibTeX entry |
| [1429] | J. von Neumann. Über adjungierte Funktionaloperatoren.
Ann. of Math., 33:294-310, 1932. BibTeX entry |
| [1430] | J. von Neumann. On regular rings. Proc. Nat. Acad. Sci. U.S.A.
, 33:294-310, 1936. BibTeX entry |
| [1431] | J. von Neumann. Some matrix inequalities and metrization of matric-space.
Tomsk Univ. Rev., 1:286-300, 1937. (Republished in John von
Neumann Collected Works, MacMillan, New York, Vol IV, pp. 205-219). BibTeX entry |
| [1432] | J. von Neumann. Functional Operators. Vol II: The Geometry of
Orthogonal Spaces, volume 29 of Annals of Math. Studies. Princeton
University Press, Princeton, 1950. BibTeX entry |
| [1433] | J. von Neumann. Continuous Geometry. Princeton University
Press, Princeton, 1960. BibTeX entry |
| [1434] | T. G. Newman, M. Meicler, and P. L. Odell. On the concept of a
p-q generalized inverse of a matrix. In Boullion and Odell
[255]
, pages 276-282. BibTeX entry |
| [1435] | T. G. Newman and P. L. Odell. On the concept of a p-q
generalized inverse of a matrix. SIAM J. Appl. Math., 17:520-525,
1969. BibTeX entry |
| [1436] | Y. Nievergelt. Total least squares: state-of-the-art regression in
numerical analysis. SIAM Rev., 36(2):258-264, 1994. BibTeX entry |
| [1437] | Y. Nievergelt. Computing circles and spheres of arithmetic least
squares. Comput. Phys. Comm., 81(3):343-350, 1994. (extension
of [1382]
). BibTeX entry |
| [1438] | Y. Nievergelt. Schmidt-Mirsky matrix approximation with linearly
constrained singular values. Linear Algebra and its Applications
, 261:207-219, 1997. BibTeX entry |
| [1439] | Y. Nievergelt. A tutorial history of least squares with applications
to astronomy and geodesy. J. Comput. Appl. Math., 121(1-2):37-72,
2000. BibTeX entry |
| [1440] | Xing Wen Niu. Plücker coordinates representation for relations
and operations between linear subspaces. J. Math. Res. Exposition
, 21(1):143-147, 2001. BibTeX entry |
| [1441] | B. Noble. A method for computing the generalized inverse of a matrix.
SIAM J. Numer. Anal., 3:582-584, 1966. BibTeX entry |
| [1442] | B. Noble. Applied Linear Algebra. Prentice-Hall, Inc., Englewood
Cliffs, NJ, 1969. BibTeX entry |
| [1443] | B. Noble. Methods for computing the Moore-Penrose generalized inverse,
and related matters. In Nashed [1402]
, pages 245-301. BibTeX entry |
| [1444] | K. Nomakuchi. On characterization of generalized inverses. Linear
Algebra and its Applications, 33:1-8, 1980. BibTeX entry |
| [1445] | K. Nordström. Some further aspects of the Löwner-ordering
antitonicity of the Moore-Penrose inverse. Comm. Statist. Theory Methods
, 18(12):4471-4489 (1990), 1989. BibTeX entry |
| [1446] | R. L. Obenchain. Good and optimal ridge estimators. The Annals
of Statist., 6(5):1111-1121, 1978. BibTeX entry |
| [1447] | P. L. Odell and T. L. Boullion. Simultaneous diagonalization of rectangular
matrices. Comput. Math. Appl., 33(9):93-96, 1997. BibTeX entry |
| [1448] | P. L. Odell and H. P. Decell, Jr. On computing the fixed-point probability
vector of ergodic transition matrices. J. Assoc. Comput. Mach.
, 14:765-768, 1967. BibTeX entry |
| [1449] | W. Oktaba. Tests of hypotheses for the fixed model not of full rank.
Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys.,
16:409-413, 1968. BibTeX entry |
| [1450] | D. P. O'Leary. On bounds for scaled projections and pseudo-inverses.
Linear Algebra and its Applications, 132:115-117, 1990. (Answer
to a question in [1770]
). BibTeX entry |
| [1451] | I. Olkin. The density of the inverse and pseudo-inverse of a random
matrix. Statist. Probab. Lett., 38(2):131-135, 1998. (alternative
proof to [2098]
). BibTeX entry |
| [1452] | J. M. Ortega and W. C. Rheinboldt. Iterative Solution of Nonlinear
Equations in Several Variables. Academic Press, New York, 1970. BibTeX entry |
| [1453] | E. E. Osborne. On least squares solutions of linear equations.
J. Assoc. Comput. Mach., 8:628-636, 1961. BibTeX entry |
| [1454] | E. E. Osborne. Smallest least squares solutions of linear equations.
SIAM J. Numer. Anal., 2:300-307, 1965. BibTeX entry |
| [1455] | M. R. Osborne. A class of methods for minimising a sum of squares.
Austral. Comput. J., 4:164-169, 1972. BibTeX entry |
| [1456] | A. Ostrowski. A new proof of Haynsworth's quotient formula for Schur
complements. Linear Algebra and its Applications, 4:389-392, 1971. BibTeX entry |
| [1457] | D. V. Ouellette. Schur complements and statistics. Linear Algebra
and its Applications, 36:187-295, 1981. BibTeX entry |
| [1458] | C. C. Paige and M. A. Saunders. Least squares estimation of discrete
linear dynamic systems using orthogonal transformations. SIAM J. Numer.
Anal., 14(2):180-193, 1977. BibTeX entry |
| [1459] | C. C. Paige and M. A. Saunders. Towards a generalized singular value
decomposition. SIAM J. Numer. Anal., 18:398-405, 1981. BibTeX entry |
| [1460] | C.-T. Pan. On the existence and computation of rank-revealing
LU factorizations. Linear Algebra and its Applications
, 316(1-3):199-222, 2000. BibTeX entry |
| [1461] | C.-T. Pan and K. Sigmon. A bottom-up inductive proof of the singular
value decomposition. SIAM J. Matrix Anal. Appl., 15(1):59-61, 1994. BibTeX entry |
| [1462] | Ping Qi Pan and Zi Xiang Ouyang. Moore-Penrose inverse simplex algorithms
based on successive linear subprogramming approach. Numer. Math. J.
Chinese Univ. (English Ser.), 3(2):180-190, 1994. BibTeX entry |
| [1463] | V. Pan and R. S. R. Schreiber. An improved newton iteration for the
generalized inverse of a matrix with applications. SIAM J. Sci. Statist.
Comput., 12:1109-1130, 1991. BibTeX entry |
| [1464] | L. Pandolfi. Controllability and stabilization for linear systems
of algebraic and differential equations. J. Optim. Theory Appl.
, 30(4):601-620, 1980. BibTeX entry |
| [1465] | B. N. Parlett. The LU and QR algorithms. In Ralston
and Wilf [1556]
, pages 116-130, Vol. II. BibTeX entry |
| [1466] | K. H. Parshall. Eliakim Hastings Moore and the founding of a mathematical
community in America. Annals of Science, 41:313-333, 1984. (reprinted
in A Century of Methematics in America - Part II, ed. Peter Duren
et al, American Mathematical Society, 1989, pp. 155-175). BibTeX entry |
| [1467] | K. H. Parshall and D. E. Rowe. The Emergence of the American Mathematical
Research Community, 1876-1900: J. J. Sylvester, Felix Klein, and E. H.
Moore. American Mathematical Society, Providence, RI, 1994. BibTeX entry |
| [1468] | S. Pati. Moore-Penrose inverse of matrices on idempotent semirings.
SIAM J. Matrix Anal. Appl., 22(2):617-626 (electronic), 2000. BibTeX entry |
| [1469] | M. Pavel-Parvu and A. Korganoff. Iteration functions for solving
polynomial equations. In B. Dejon and P. Henrici, editors, Constructive
Aspects of the Fundamental Theorem of Algebra, New York, 1969. John
Wiley. BibTeX entry |
| [1470] | G. Peano. Intégration par séries des équations
différentielles linéaires. Mathematische Annallen
, 32:450-456, 1888. BibTeX entry |
| [1471] | M. H. Pearl. On Cayley's parametrization. Canad. J. Math.
, 9:553-562, 1957. BibTeX entry |
| [1472] | M. H. Pearl. A further extension of Cayley's parametrization.
Canad. J. Math., 11:48-50, 1959. BibTeX entry |
| [1473] | M. H. Pearl. On normal and EPr matrices.
Michigan Math. J., 6:1-5, 1959. BibTeX entry |
| [1474] | M. H. Pearl. On normal EPr matrices. Michigan
Math. J., 8:33-37, 1961. BibTeX entry |
| [1475] | M. H. Pearl. On generalized inverses of matrices. Proc. Cambridge
Philos. Soc., 62:673-677, 1966. BibTeX entry |
| [1476] | M. H. Pearl. A decomposition theorem for matrices. Canad. J.
Math., 19:344-349, 1967. (see [1827]
, [2053]
). BibTeX entry |
| [1477] | M. H. Pearl. Generalized inverses of matrices with entries taken
from an arbitrary field. Linear Algebra and its Applications,
1:571-587, 1968. (see also [1596]
). BibTeX entry |
| [1478] | M. H. Pearl. Automorphic transformations of an arbitrary matrix.
Linear and Multilinear Algebra, 15(3-4):245-256, 1984. BibTeX entry |
| [1479] | K. Pearson. On lines and planes of closest fit to points in space.
Philosophical Magazine, 2:559-572, 1901. BibTeX entry |
| [1480] | R. Peluso and G. Piazza. Bounds for products of singular values of
a matrix. Rend. Mat. Appl. (7), 19(4):507-522 (2000), 1999. BibTeX entry |
| [1481] | R. H. Pennington. Introductory Computer Methods and Numerical
Analysis. MacMillan Co., New York, 1970. BibTeX entry |
| [1482] | R. Penrose. A generalized inverse for matrices. Proceedings
of the Cambridge Philosophical Society, 51:406-413, 1955. BibTeX entry |
| [1483] | R. Penrose. On best approximate solutions of linear matrix equations.
Proceedings of the Cambridge Philosophical Society, 52:17-19,
1956. BibTeX entry |
| [1484] | V. Pereyra. Iterative methods for solving nonlinear least squares
problems. SIAM J. Numer. Anal., 4:27-36, 1967. BibTeX entry |
| [1485] | V. Pereyra. Stability of general systems of linear equations.
Aequationes Mathematicae, 2:194-206, 1969. BibTeX entry |
| [1486] | V. Pereyra and J. B. Rosen. Computation of the pseudoinverse of a
matrix of unknown rank. Technical Report CS 13, Dept. of Computer Science,
Stanford University, Stanford, CA, Sept. 1964. (Comp. Rev.6
(1965), 259 #7948). BibTeX entry |
| [1487] | G. Peters and J. H. Wilkinson. The least squares problem and pseudo-inverses.
Comput. J., 13:309-316, 1970. BibTeX entry |
| [1488] | W. V. Petryshyn. On generalized inverses and on the uniform convergence
of (I-beta K)n with application to iterative
methods. J. Math. Anal. Appl., 18:417-439, 1967. BibTeX entry |
| [1489] | D. L. Phillips. A technique for the numerical solution of certain
integral equations of the first kind. J. Assoc. Comput. Mach.,
9:84-97, 1962. BibTeX entry |
| [1490] | R. Picón. A systematic deduction of linear natural approach
equations. Computer Methods in Applied Mechanics and Engineering
, 177:137-151, 1999. BibTeX entry |
| [1491] | W. H. Pierce. A self-correcting matrix iteration for the Moore-Penrose
generalized inverse. Linear Algebra and its Applications, 244:357-363,
1996. BibTeX entry |
| [1492] | A. Pietsch. Zur Theorie der sigma-Transformationen in lokalkonvexen
Vektorräumen. Math. Nach., 21:347-369, 1960. BibTeX entry |
| [1493] | R. Piziak, P. L. Odell, and R. Hahn. Constructing projections on
sums and intersections. Comput. Math. Appl., 37(1):67-74, 1999. BibTeX entry |
| [1494] | R. L. Plackett. Some theorems in least squares. Biometrika
, 37:149-157, 1950. BibTeX entry |
| [1495] | R. J. Plemmons. Generalized inverses of Boolean relation matrices.
SIAM J. Appl. Math., 20:426-433, 1971. BibTeX entry |
| [1496] | R. J. Plemmons and R. E. Cline. The generalized inverse of a nonnegative
matrix. Proc. Amer. Math. Soc., 31:46-50, 1972. (erratum, ibid
39(1972), 651). BibTeX entry |
| [1497] | T. Poggio and F. Girosi. Regularization algorithms for learning that
are equivalent to multilayer networks. Science, 247(4945):978-982,
1990. BibTeX entry |
| [1498] | Olga Pokorná. On the pseudoinversion of matrix products.
In Numerical Methods (Third Colloq., Keszthely, 1977), pages 501-506.
North-Holland, Amsterdam, 1980. BibTeX entry |
| [1499] | W. Pölzleitner and H. Wechsler. Selective and focused invariant
recognition using distributed associative memories (DAM). IEEE Transactions
on Pattern Analysis and Machine Intelligence, 12(8):809-814, 1990. BibTeX entry |
| [1500] | G. D. Poole and G. P. Barker. MP matrices. Linear Algebra and
its Applications, 26:165-174, 1979. BibTeX entry |
| [1501] | G. D. Poole and T. L. Boullion. Weak spectral inverses which are
partial isometries. SIAM J. Appl. Math., 23:171-172, 1972. BibTeX entry |
| [1502] | G. D. Poole and T. L. Boullion. The Drazin inverse for certain power
matrices. Indust. Math., 22:35-37, 1972. BibTeX entry |
| [1503] | G. D. Poole and T. L. Boullion. The Drazin inverse and a spectral
inequality of Marcus, Minc, and Moyls. J. Optimization Theory Appl.
, 15:503-508, 1975. BibTeX entry |
| [1504] | W. A. Porter. Modern Foundations of System Engineering.
MacMillan, New York, 1966. BibTeX entry |
| [1505] | W. A. Porter. A basic optimization problem in linear systems.
Math. Syst. Th., 5:20-44, 1971. BibTeX entry |
| [1506] | W. A. Porter and J. P. Williams. A note on the minimum effort control
problem. J. Math. Anal. Appl., 13:251-264, 1966. BibTeX entry |
| [1507] | W. A. Porter and J. P. Williams. Extension of the minimum effort
control problem. J. Math. Anal. Appl., 13:536-549, 1966. BibTeX entry |
| [1508] | K. M. Prasad. Generalized inverses of matrices over commutative rings.
In Bapat et al. [108]
, pages 35-52. (special issue of Linear Algebra and its Applications
211 (1994)). BibTeX entry |
| [1509] | K. M. Prasad and R. B. Bapat. A note on the Khatri-inverse.
Sankhya Ser. A, 54(2):291-295, 1992. BibTeX entry |
| [1510] | K. M. Prasad and R. B. Bapat. The generalized Moore-Penrose inverse.
Linear Algebra and its Applications, 165:59-69, 1992. BibTeX entry |
| [1511] | K. M. Prasad, K. P. S. Bhaskara Rao, and R. B. Bapat. Generalized
inverses over integral domains. II. Group inverses and Drazin inverses.
Linear Algebra and its Applications, 146:31-47, 1991. BibTeX entry |
| [1512] | William K. Pratt and Faramarz Davarian. Fast computational techniques
for pseudoinverse and Wiener image restoration. IEEE Trans. Computers
, C-26(6):571-580, 1977. BibTeX entry |
| [1513] | G. B. Preston. Inverse semi-groups. J. London Math. Soc.
, 29:396-403, 1954. BibTeX entry |
| [1514] | C. M. Price. The matrix pseudoinverse and minimal variance estimates.
SIAM Rev., 6:115-120, 1964. BibTeX entry |
| [1515] | R. M. Pringle and A. A. Rayner. Expressions for generalized inverses
of a bordered matrix with application to the theory of constrained linear
models. SIAM Rev., 12:107-115, 1970. BibTeX entry |
| [1516] | R. M. Pringle and A. A. Rayner. Generalized Inverse Matrices with
Applications to Statistics. Griffin's Statistical Monographs and Courses,
No. 28. Hafner Publishing Co., New York, 1971. BibTeX entry |
| [1517] | A. J. Pritchard. The application of pseudo-inverses and fixed point
theorems in systems theory. Bull. Inst. Math. Appl., 19(5-6):110-115,
1983. BibTeX entry |
| [1518] | D. Przeworska-Rolewicz and S. Rolewicz. Equations in Linear Spaces
, volume 47 of Polska Akad. Nauk Monog. Mat. PWN Polish Scientific
Publishers, Warsaw, 1968. BibTeX entry |
| [1519] | A. C. Pugh and Liansheng Tan. A generalized chain-scattering representation
and its algebraic system properties. IEEE Trans. Automat. Control
, 45(5):1002-1007, 2000. BibTeX entry |
| [1520] | P. Pulay and G. Fogarasi. Geometry optimization in redundant internal
coordinates. The Journal of Chemical Physics, 96(4):2856-2860, 1992.
(see [1237]
). BibTeX entry |
| [1521] | S. Puntanen and A. J. Scott. Some further remarks on the singular
linear model. Linear Algebra and its Applications, 237/238:313-327,
1996. BibTeX entry |
| [1522] | S. Puntanen and G. P. H. Styan. The equality of the ordinary least
squares estimator and the best linear unbiased estimator (with comments
by O. Kempthorne and S. R. Searle and a reply by the authors). Amer.
Statist., 43(3):153-164, 1989. BibTeX entry |
| [1523] | S. Puntanen, G. P. H. Styan, and H. -J. Werner. Two matrix-based
proofs that the linear estimator Gy is the best linear unbiased
estimator. J. Statist. Plann. Inference, 88(2):173-179, 2000. BibTeX entry |
| [1524] | M. L. Puri, C. T. Russell, and T. Mathew. Convergence of generalized
inverses with applications to asymptotic hypothesis testing. Sankhya
Ser. A, 46(2):277-286, 1984. BibTeX entry |
| [1525] | R. Puystjens. Moore-Penrose inverses for matrices over some Noetherian
rings. J. Pure Appl. Algebra, 31(1-3):191-198, 1984. BibTeX entry |
| [1526] | R. Puystjens. Some aspects of generalized invertibility. Bull.
Soc. Math. Belg. Sér. A, 40(1):67-72, 1988. BibTeX entry |
| [1527] | R. Puystjens and R. E. Hartwig. The group inverse of a companion
matrix. Linear and Multilinear Algebra, 43(1-3):137-150, 1997. BibTeX entry |
| [1528] | R. Puystjens and D. W. Robinson. The Moore-Penrose inverse of a morphism
with factorization. Linear Algebra and its Applications, 40:129-141,
1981. BibTeX entry |
| [1529] | R. Puystjens and D. W. Robinson. The Moore-Penrose inverse of a morphism
in an additive category. Comm. Algebra, 12(3-4):287-299, 1984.
(see [781]
). BibTeX entry |
| [1530] | R. Puystjens and D. W. Robinson. Symmetric morphisms and the existence
of Moore-Penrose inverses. Linear Algebra and its Applications,
131:51-69, 1990. BibTeX entry |
| [1531] | R. Puystjens and H. de Smet. The Moore-Penrose inverse for matrices
over skew polynomial rings. In Ring Theory, Antwerp 1980 (Proc. Conf.,
Univ. Antwerp, Antwerp, 1980), pages 94-103. Springer, Berlin, 1980. BibTeX entry |
| [1532] | W. C. Pye. Nonnegative Drazin inverses. Linear Algebra and its
Applications, 30:149-153, 1980. BibTeX entry |
| [1533] | W. C. Pye, T. L. Boullion, and T. A. Atchison. The pseudoinverse
of a composite matrix of circulants. SIAM J. Appl. Math., 24:552-555,
1973. BibTeX entry |
| [1534] | W. C. Pye, T. L. Boullion, and T. A. Atchison. The pseudoinverse
of a centrosymmetric matrix. Linear Algebra and its Applications
, 6:201-204, 1973. BibTeX entry |
| [1535] | L. D. Pyle. Generalized inverse computations using the gradient projection
method. J. Assoc. Comput. Mach., 11:422-428, 1964. BibTeX entry |
| [1536] | L. D. Pyle. A generalized inverse varepsilon -algorithm for
constructing intersection projection matrices, with applications.
Numer. Math., 10:86-102, 1967. BibTeX entry |
| [1537] | L. D. Pyle. The generalized inverse in linear programming. Basic
structure. SIAM J. Appl. Math., 22:335-355, 1972. BibTeX entry |
| [1538] | L. D. Pyle and R. E. Cline. The generalized inverse in linear programming-interior
gradient projection methods. SIAM. J. Appl. Math., 24:511-534,
1973. BibTeX entry |
| [1539] | Yu. P. Pyt'ev. A pseudoinverse operator. Properties and applications.
Mat. Sb. (N.S.), 118(160)(1):19-49, 143, 1982. BibTeX entry |
| [1540] | P. Rabinowitz (editor). Numerical Methods for Nonlinear Algebraic
Equations. Gordon and Breach, London, 1970. BibTeX entry |
| [1541] | G. Rabson. The generalized inverse in set theory and matrix theory.
Technical report, Dept. of Mathematics, Clarkson College of Technology,
Potsdam, NY, 1969. BibTeX entry |
| [1542] | M. Radic. A definition of the determinant of a rectangular matrix.
Glasnik Mat. Ser. III, 1 (21):17-22, 1966. BibTeX entry |
| [1543] | M. Radic. On a generalization of the Arghiriade-Dragomir representation
of the Moore-Penrose inverse. Atti Accad. Naz. Lincei Rend. Cl. Sci.
Fis. Mat. Natur. (8), 44:333-336, 1968. BibTeX entry |
| [1544] | R. Rado. Note on generalized inverses of matrices. Proceedings
of the Cambridge Philosophical Society, 52:600-601, 1956. BibTeX entry |
| [1545] | M. Abdur Rahman. Representation of Moore-Penrose generalized inverse
of the product of two matrices. Ganit. Journal of Bangladesh Mathematical
Society, 13(1-2):83-85, 1993. BibTeX entry |
| [1546] | V. Rakocevic. Moore-Penrose inverse in Banach algebras. Proc.
Roy. Irish Acad. Sect. A, 88(1):57-60, 1988. BibTeX entry |
| [1547] | V. Rakocevic. On the continuity of the Moore-Penrose inverse in Banach
algebras. Facta Univ. Ser. Math. Inform., (6):133-138, 1991. BibTeX entry |
| [1548] | V. Rakocevic. Continuity of the Drazin inverse. J. Operator
Theory, 41(1):55-68, 1999. BibTeX entry |
| [1549] | V. Rakocevic. Continuity, differentiability and perturbations of
the Drazin inverse. In Proceedings of the 10th Congress of Yugoslav
Mathematicians (Belgrade, 2001), pages 99-112. Univ. Belgrade Fac.
Math., Belgrade, 2001. BibTeX entry |
| [1550] | V. Rakocevic and Yimin Wei. The perturbation theory for the Drazin
inverse and its applications II. J. Austral. Math. Soc., 70(2):189-197,
2001. BibTeX entry |
| [1551] | V. Rakocevic and Yimin Wei. The perturbation theory for the Drazin
inverse and its applications. II. J. Aust. Math. Soc., 70(2):189-197,
2001. BibTeX entry |
| [1552] | Vladimir Rakocevic and Yimin Wei. A weighted Drazin inverse and applications.
Linear Algebra and its Applications, 350:25-39, 2002. BibTeX entry |
| [1553] | M. Rakowski. Generalized pseudoinverses of matrix valued functions.
Integral Equations Operator Theory, 14(4):564-585, 1991. BibTeX entry |
| [1554] | L. B. Rall. Computational Solution of Nonlinear Operator Equations
. Wiley, New York, 1969. BibTeX entry |
| [1555] | A. Ralston and P. Rabinowitz. A First Course in Numerical Analysis
(2nd edition). McGraw-Hill, New York, 1978. BibTeX entry |
| [1556] | A. Ralston and H. Wilf, editors. Mathematical Methods for Digital
Computers, New York, 1967. Wiley. BibTeX entry |
| [1557] | K. G. Ramamurthy and S. R. Mohan. Nonnegativity of principal minors
of generalized inverses of p0-matrices. Linear Algebra
and its Applications, 65:125-131, 1985. BibTeX entry |
| [1558] | J. H. Randall and A. A. Rayner. The accuracy of least squares calculations
with the Cholesky algorithm. Linear Algebra and its Applications
, 127:463-502, 1990. BibTeX entry |
| [1559] | C. R. Rao. Markoff's theorem with linear restrictions on parameters.
Sankhya Ser. A, 7:16-20, 1945. BibTeX entry |
| [1560] | C. R. Rao. A note on a generalized inverse of a matrix with applications
to problems in mathematical statistics. J. Roy. Statist. soc. Ser.
B, 24:152-158, 1962. BibTeX entry |
| [1561] | C. R. Rao. Linear Statistical Inference and its Applications
. J. Wiley & Sons, New York, 1965. (Second edition, 1973). BibTeX entry |
| [1562] | C. R. Rao. Generalized inverse for matrices and its applications
in mathematical statistics. In Research Papers in Statistics (Festschrift
J. Neyman), pages 263-279. Wiley, London, 1966. BibTeX entry |
| [1563] | C. R. Rao. Calculus of generalized inverses of matrices, part I:
General theory. Sankhya Ser. A, 29:317-342, 1967. BibTeX entry |
| [1564] | C. R. Rao. Unified theory of linear estimation. Sankhya Ser.
A, 33:371-394, 1971. (see [1565]
, [1566]
). BibTeX entry |
| [1565] | C. R. Rao. Corrigendum: ``Unified theory of linear estimation'' (Sankhya
Ser. A 33 (1971), 371-394). Sankhya Ser. A, 34:194, 1972. BibTeX entry |
| [1566] | C. R. Rao. Corrigenda: ``Unified theory of linear estimation'' (Sankhya
Ser. A 33 (1971), 371-394). Sankhya Ser. A, 34:477, 1972. BibTeX entry |
| [1567] | C. R. Rao. Projectors, generalized inverses and the bl
ue's. J. Roy. Statist. Soc. Ser. B, 36:442-448, 1974. BibTeX entry |
| [1568] | C. R. Rao. Estimation of parameters in a linear model (first 1975
Wald memorial lecture). Ann. Statist., 4(6):1023-1037, 1976.
(see [1570]
). BibTeX entry |
| [1569] | C. R. Rao. Choice of best linear estimators in the Gauss-Markoff
model with a singular dispersion matrix. Comm. Statist. A-Theory Methods
, 7(13):1199-1208, 1978. BibTeX entry |
| [1570] | C. R. Rao. Correction to: ``Estimation of parameters in a linear
model'' (Ann. Statist. 4 (1976), no. 6, 1023-1037). Ann. Statist.
, 7(3):696, 1979. BibTeX entry |
| [1571] | C. R. Rao. A lemma on g-inverse of a matrix and computation of correlation
coeffiecients in the singular case. Communications in Statistics (A)
, 10:1-10, 1981. BibTeX entry |
| [1572] | C. R. Rao. The inefficiency of least squares: extensions of the Kantorovich
inequality. Linear Algebra and its Applications, 70:249-255, 1985. BibTeX entry |
| [1573] | C. R. Rao. Linear transformations, projection operators and generalized
inverses: a geometric approach. In Contributions to Stochastics
, pages 1-10. Wiley, New York, 1992. BibTeX entry |
| [1574] | C. R. Rao and S. K. Mitra. Generalized Inverse of Matrices and
Its Applications. John Wiley, New York, 1971. BibTeX entry |
| [1575] | C. R. Rao and S. K. Mitra. Theory and application of constrained
inverse of matrices. SIAM J. Appl. Math., 24:473-488, 1973. BibTeX entry |
| [1576] | C. R. Rao, S. K. Mitra, and P. Bhimasankaram. Determination of a
matrix by its subclasses of generalized inverses. Sankhya Ser. A
, 34:5-8, 1972. BibTeX entry |
| [1577] | C. R. Rao and H. Yanai. General definition and decomposition of projectors
and some applications to statistical problems. J. Statist. Plann.
Inference, 3:1-17, 1979. BibTeX entry |
| [1578] | C. R. Rao and H. Yanai. Generalized inverse of linear transformations:
a geometric approach. Linear Algebra and its Applications, 66:87-98,
1985. BibTeX entry |
| [1579] | C. R. Rao and H. Yanai. Generalized inverses of partitioned matrices useful in statistical applications. Linear Algebra and its Applications |