| [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 |