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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT 257 37 "Iterative Solutions of L
inear Systems" }}{PARA 20 "" 0 "" {TEXT 258 62 "Linear Algebra and Its
 Applications  by David C. Lay  page 143" }{MPLTEXT 0 21 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 
32 "Warning, new definition for norm" }}{PARA 7 "" 1 "" {TEXT -1 33 "W
arning, new definition for trace" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 40 "A:=matrix(3,3,[10,1,-1,1,15,1,-1,1,20]);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7%7%\"#5\"\"\"!\"\"7%F+\"#:F+
7%F,F+\"#?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "A[2,2];" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 59 "G:=matrix(3,3,proc(i,j) if i>=j then A[i,j] else 0 fi
 end);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"GG-%'matrixG6#7%7%\"#5\"
\"!F+7%\"\"\"\"#:F+7%!\"\"F-\"#?" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 58 "J:=matrix(3,3,proc(i,j) if j=i then A[i,j] else 0 fi \+
end);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"JG-%'matrixG6#7%7%\"#5\"
\"!F+7%F+\"#:F+7%F+F+\"#?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
32 "Y:=matrix(3,1,[y[1],y[2],y[3]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>%\"YG-%'matrixG6#7%7#&%\"yG6#\"\"\"7#&F+6#\"\"#7#&F+6#\"\"$" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "X:=matrix(3,1,[x[1],x[2],x[3
]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"XG-%'matrixG6#7%7#&%\"xG6#
\"\"\"7#&F+6#\"\"#7#&F+6#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 27 "B:=matrix(3,1,[18,-12,17]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%\"BG-%'matrixG6#7%7#\"#=7#!#77#\"#<" }}}{EXCHG {PARA 0 "" 0 "" 
{MPLTEXT 0 21 54 "The System of Linear Equations in Gauss-Seidel Metho
d." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "N:=evalm(G-A);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG-%'matrixG6#7%7%\"\"!!\"\"\"\"\"
7%F*F*F+7%F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "evalm(G
&*Y=N&*X + B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%'matrixG6#7%7#,$&
%\"yG6#\"\"\"\"#57#,&F*F-&F+6#\"\"#\"#:7#,(F*!\"\"F1F-&F+6#\"\"$\"#?-F
%6#7%7#,(&%\"xGF2F7&FBF9F-\"#=F-7#,&FCF7!#7F-7#\"#<" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 21 "A:=augment(G,N&*X+B);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7%7&\"#5\"\"!F+,(&%\"xG6#\"\"#!\"\"
&F.6#\"\"$\"\"\"\"#=F57&F5\"#:F+,&F2F1!#7F57&F1F5\"#?\"#<" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "E:=rref(%);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"EG-%'matrixG6#7%7&\"\"\"\"\"!F+,(&%\"xG6#\"\"$#F*\"
#5#\"\"*\"\"&F*&F.6#\"\"##!\"\"F27&F+F*F+,(#!#B\"#DF*F-#!#6\"$]\"F6#F*
FB7&F+F+F*,(F6#!\"#\"$v$F-#\"#8\"%+:#\"$$\\\"$+&F*" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 11 "backsub(E);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#-%'vectorG6#7%,(&%\"xG6#\"\"$#\"\"\"\"#5#\"\"*\"\"&F-&F)6#\"\"##
!\"\"F.,(#!#B\"#DF-F(#!#6\"$]\"F2#F-F=,(F2#!\"#\"$v$F(#\"#8\"%+:#\"$$
\\\"$+&F-" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 35 "The following i
s a Jacobi's Method." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "rest
art;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}
{PARA 7 "" 1 "" {TEXT -1 32 "Warning, new definition for norm" }}
{PARA 7 "" 1 "" {TEXT -1 33 "Warning, new definition for trace" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 389 "JA:=proc(n::nonnegint)\nopt
ion remember;\nlocal sol, A, M, N, B, X, i, C; \nA:=matrix(3,3,[10,1,-
1,1,15,1,-1,1,20]);\nM:=matrix(3,3,proc(i,j) if j=i then A[i,j] else 0
 fi end);\nN:=M-A;\nB:=matrix(3,1,[18,-12,17]);\nX:= matrix(3,1,[0,0,0
]);\nfor i  from 0 to n \n    do\nC:=augment(M,evalm(N&*X)+B);        \+
                                                    X:=evalf(backsub(r
ref(C)));\n    od;\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 
"seq(JA(i),i=0..15);" }}{PARA 12 "" 1 "" {XPPMATH 20 "62-%'vectorG6#7%
$\"+++++=!\"*$!+++++!)!#5$\"+++++&)F,-F$6#7%$\"++++l>F)$!+nmmm(*F,$\"+
++++)*F,-F$6#7%$\"+nmm&*>F)$!+LLLj**F,$\"+NL$3(**F,-F$6#7%$\"+n;M**>F)
$!+nm;&***F,$\"++++'***F,-F$6#7%$\"+n;\"***>F)$!+ZWH****F,$\"+l\"H%***
*F,-F$6#7%$\"+Os)***>F)$!+`I!*****F,$\"+b0#*****F,-F$6#7%$\"+O#)****>F
)$!+$>')*****F,$\"+q())*****F,-F$6#7%$\"+](*****>F)$!+t!)******F,$\"+I
%)******F,-F$6#7%$\"+l******>F)$!+F(*******F,$\"+!y*******F,-F$6#7%$\"
+&*******>F)$!+g********F,$\"+q********F,-F$6#7%$\"+********>F)$!+$***
******F,$\"+&*********F,-F$6#7%$\"+++++?F)$!+++++5F)$\"+++++5F)FcqFcqF
cqFcq" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 39 "The following is a \+
Gauss-Seidel Method." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "rest
art;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}
{PARA 7 "" 1 "" {TEXT -1 32 "Warning, new definition for norm" }}
{PARA 7 "" 1 "" {TEXT -1 33 "Warning, new definition for trace" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 410 "GS:=proc(n::nonnegint)\nopt
ion remember;\nlocal sol, A, M, N, B, X, i, C; \nA:=matrix(3,3,[10,1,-
1,1,15,1,-1,1,20]);\nM:=matrix(3,3,proc(i,j) if j<=i then A[i,j] else \+
0 fi end);\nN:=M-A;\nB:=matrix(3,1,[18,-12,17]);\nX:= matrix(3,1,[0,0,
0]);\nfor i from 0 to n \n    do\nC:=augment(M,evalm(N&*X)+B);        \+
                                                                      \+
   X:=evalf(backsub(rref(C)));\n    od;\nend:" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 19 "seq(GS(i), i=0..6);" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6)-%'vectorG6#7%$\"+++++=!\"*$!+++++#*!#5$\"++++g)*F,-F$6
#7%$\"+++g!*>F)$!+++S%)**F,$\"+++_%***F,-F$6#7%$\"++#*y**>F)$!+LT\\***
*F,$\"+0$p)****F,-F$6#7%$\"+MO****>F)$!+Sq)*****F,$\"+lh******F,-F$6#7
%$\"+K)*****>F)$!+L'*******F,$\"+&*)*******F,-F$6#7%$\"+&*******>F)$!+
$*********F,$\"+++++5F)-F$6#7%$\"+++++?F)$!+++++5F)FZ" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 37 }{VIEWOPTS 1 
1 0 1 1 1803 }