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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "restart:with(linalg)
:with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 32 "Warning, new definition \+
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race" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "GradNext:=proc(f,x,
x0)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "local gr,valf,step;" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "gr:=eval(grad(f,x),x=x0):valf:=eval
(f,x=x0):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "step:=valf/(norm(gr,2)
)^2:evalm(x0-step*gr);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "x:=array(1..2):GradNext(x[1]
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x0:valf:=eval(f,x=x0):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "lprint(IT
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(function):print(valf):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "for k fr
om 1 to N do " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "   sol[k]:=GradNex
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "GradIter:=proc(f,x,x0,N)" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "local k,sol,valf;" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 47 "sol:=array(0..N):sol[0]:=x0:valf:=eval(f,x=x0):
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "   sol[k]:=NewtonGradNext(f,x,sol[k
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "NewtonGradNext:=proc(f,x,x0)" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "local gr,hess,hessinv,step;" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "gr:=eval(grad(f,x),x=x0):" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 53 "hess:=subs(x=x0,hessian(f,x)):hessinv:=in
verse(hess);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "step:=1:evalm(x0-st
ep*(hessinv &* gr));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "x:=array(1..2):NewtonGradNex
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rG6#7$#\"\"\"\"\"#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "
NewtonGrads:=proc(f,x,x0,N)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "loca
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rint(ITERATION,0):print(sol[0]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 
"lprint(function):print(valf):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "f
or k from 1 to N do " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "   sol[k]:=
NewtonGradNext(f,x,sol[k-1]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "  \+
 valf:=eval(f,x=sol[k]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "   lpri
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d:end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "NewtonGrad:=proc(
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "sol:=array(0..N):sol[0]:=x0:valf:=e
val(f,x=x0):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "lprint(ITERATION,0)
:print(sol[0]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "lprint(function)
:print(valf):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "for k from 1 to N \+
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x,sol[k-1]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "   valf:=eval(f,x=s
ol[k]):od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "   lprint(ITERATION,k
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "x:=array(1..2):NewtonGrad(x[
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{PARA 6 "" 1 "" {TEXT -1 8 "function" }}{PARA 11 "" 1 "" {XPPMATH 20 "
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{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7$$\"+Q!4'))y!#S\"\"!" }}
{PARA 6 "" 1 "" {TEXT -1 8 "function" }}{PARA 11 "" 1 "" {XPPMATH 20 "
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}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "local i,s; global x;" }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 29 "x:=array(1..n);s:=(1-x[1])^2;" }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 22 "for i from 1 to n-1 do" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 30 "s:=s+100*(x[i]-x[i+1]^2)^2 od;" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Ros
enbrock(2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$),&\"\"\"F'&%\"xG6#
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "x:=array(1..2):GradIter(Rosenbrock(
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{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"\")!\"\"$\"\"#F&" }}{PARA 6 "" 1 
"" {TEXT -1 8 "function" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"'+!y&!\"
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{XPPMATH 20 "6#-%'vectorG6#7$$\"+(4!*4!**!#7\"\"!" }}{PARA 6 "" 1 "" 
{TEXT -1 8 "function" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+*4!*4!**!#
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rock(2),x[1]=-1..1.5,x[2]=0..1.5,scaling=constrained,grid=[100,100],co
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "#display(A);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "NewtonGradSolSet:=proc(f,x,x0,N)" }
}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "local n,sol,k;global NGsolset;" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "n:=vectdim(x0):sol:=array(0..N):sol
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from 1 to N do " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "   sol[k]:=Newto
nGradNext(f,x,sol[k-1]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "   NGso
lset:=augment(NGsolset,sol[k]):od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
8 "    end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "x:=array(1..
2):f:=Rosenbrock(2):NewtonGradSolSet(f,x,[0.4,0.8],100):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "B:=pointplot(NGsolset,connect=false
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14 "#display(A,B);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "GradS
olSet:=proc(f,x,x0,N)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "local n,so
l,k;global Gsolset;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "n:=vectdim(x
0):sol:=array(0..N):sol[0]:=x0:Gsolset:=sol[0]:" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "for k from 1 to N do " }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 34 "   sol[k]:=GradNext(f,x,sol[k-1]):" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 39 "   Gsolset:=augment(Gsolset,sol[k]):od:" }}{PARA 0 ">
 " 0 "" {MPLTEXT 1 0 8 "    end:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 62 "x:=array(1..2):f:=Rosenbrock(2):GradSolSet(f,x,[0.4,0
.8],100):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "C:=pointplot(G
solset,connect=false,symbol=CIRCLE,color=BLUE):" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 14 "#display(A,C);" }}}{EXCHG {PARA 0 "> " 0 "" 
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