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0 0 0 1 }{PSTYLE "_pstyle3" -1 202 1 {CSTYLE "" -1 -1 "Courier" 1 12 255 0 0 1 0 1 0 2 1 2 0 0 0 1 }0 0 0 -1 -1 -1 1 0 1 0 2 2 -1 1 } {PSTYLE "_pstyle4" -1 203 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{CSTYLE "_cstyle3" -1 204 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{PSTYLE "_pstyle5" -1 204 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }0 0 0 -1 -1 -1 1 0 1 0 2 2 -1 1 }{CSTYLE "_cstyle4" -1 205 "Times" 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }} {SECT 0 {EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 20 "#Andrew Sommese \+ 2004" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 8 "restart;" } {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 20 "w ith(LinearAlgebra);" }{MPLTEXT 1 202 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#7brI#&xG6\"I$AddG6$I*protectedGF(I(_syslibGF%I(AdjointG F%I3BackwardSubstituteGF%I+BandMatrixGF%I&BasisGF%I-BezoutMatrixGF%I/B idiagonalFormGF%I-BilinearFormGF%I5CharacteristicMatrixGF%I9Characteri sticPolynomialGF%I'ColumnGF%I0ColumnDimensionGF%I0ColumnOperationGF%I, ColumnSpaceGF%I0CompanionMatrixGF%I0ConditionNumberGF%I/ConstantMatrix GF%I/ConstantVectorGF%I%CopyGF%I2CreatePermutationGF%I-CrossProductGF% I-DeleteColumnGF%I*DeleteRowGF%I,DeterminantGF%I)DiagonalGF%I/Diagonal MatrixGF%I*DimensionGF%I+DimensionsGF%I+DotProductGF%I6EigenConditionN umbersGF%I,EigenvaluesGF%I-EigenvectorsGF%I&EqualGF%I2ForwardSubstitut eGF%I.FrobeniusFormGF%I4GaussianEliminationGF%I2GenerateEquationsGF%I/ GenerateMatrixGF%I2GetResultDataTypeGF%I/GetResultShapeGF%I5GivensRota tionMatrixGF%I,GramSchmidtGF%I-HankelMatrixGF%I,HermiteFormGF%I3Hermit ianTransposeGF%I/HessenbergFormGF%I.HilbertMatrixGF%I2HouseholderMatri xGF%I/IdentityMatrixGF%I2IntersectionBasisGF%I+IsDefiniteGF%I-IsOrthog onalGF%I*IsSimilarGF%I*IsUnitaryGF%I2JordanBlockMatrixGF%I+JordanFormG F%I(LA_MainGF%I0LUDecompositionGF%I-LeastSquaresGF%I,LinearSolveGF%I$M apGF%I%Map2GF%I*MatrixAddGF%I2MatrixExponentialGF%I/MatrixFunctionGF%I .MatrixInverseGF%I5MatrixMatrixMultiplyGF%I+MatrixNormGF%I,MatrixPower GF%I5MatrixScalarMultiplyGF%I5MatrixVectorMultiplyGF%I2MinimalPolynomi alGF%I&MinorGF%I(ModularGF%I)MultiplyGF'I,NoUserValueGF%I%NormGF'I*Nor malizeGF%I*NullSpaceGF%I3OuterProductMatrixGF%I*PermanentGF%I&PivotGF% I*PopovFormGF%I0QRDecompositionGF%I-RandomMatrixGF%I-RandomVectorGF%I% RankGF%I6RationalCanonicalFormGF%I6ReducedRowEchelonFormGF%I$RowGF%I-R owDimensionGF%I-RowOperationGF%I)RowSpaceGF%I-ScalarMatrixGF%I/ScalarM ultiplyGF%I-ScalarVectorGF%I*SchurFormGF%I/SingularValuesGF%I*SmithFor mGF%I*SubMatrixGF%I*SubVectorGF%I)SumBasisGF%I0SylvesterMatrixGF%I/Toe plitzMatrixGF%I&TraceGF'I*TransposeGF%I0TridiagonalFormGF%I+UnitVector GF%I2VandermondeMatrixGF%I*VectorAddGF%I,VectorAngleGF%I5VectorMatrixM ultiplyGF%I+VectorNormGF%I5VectorScalarMultiplyGF%I+ZeroMatrixGF%I+Zer oVectorGF%I$ZipGF%" }{TEXT 203 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 28 "A:= Matrix([ [4.0,1.0,1.0]," }{MPLTEXT 1 202 0 "" }}{PARA 202 "> " 0 "" {MPLTEXT 1 0 28 " [1.0,3.0,1.0]," } {MPLTEXT 1 0 0 "" }}{PARA 202 "> " 0 "" {MPLTEXT 1 0 31 " \+ [1.0,2.0,5.0] ]);" }{MPLTEXT 1 0 0 "" }}{PARA 200 "> " 0 "" {MPLTEXT 1 202 18 "b:= <1.0,2.0,3.0>;" }{MPLTEXT 1 202 0 "" }}{PARA 200 "> " 0 "" {MPLTEXT 1 202 20 "z:=LinearSolve(A,b);" }{MPLTEXT 1 202 0 "" }} {PARA 201 "" 1 "" {XPPMATH 20 "6#>I\"AG6\"-I'RTABLEGF%6%\"'S:b-I'MATRI XGF%6#7%7%$\"#S!\"\"$\"#5F1F27%F2$\"#IF1F27%F2$\"#?F1$\"#]F1I'MatrixG6 $I*protectedGF>I(_syslibGF%" }{TEXT 203 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#>I\"bG6\"-I'RTABLEGF%6%\"'G*z$-I'MATRIXGF%6#7%7#$\"#5! \"\"7#$\"#?F17#$\"#IF1&I'VectorG6$I*protectedGF;I(_syslibGF%6#I'column GF%" }{TEXT 203 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#>I\"zG6\"-I'RT ABLEGF%6%\"'o*z$-I'MATRIXGF%6#7%7#$\"3j#3oWdfw7#!#>7#$\"3n7-`!# =7#$\"3s`D/MsyHQF5&I'VectorG6$I*protectedGF " 0 "" {MPLTEXT 1 202 37 "#Dia g := DiagonalMatrix(Diagonal(A));" }{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 23 "#B:=MatrixAdd(A,-Diag);" } {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 203 "" 0 "" {TEXT 204 76 "The foll owing uses the Jacobi method to iteratively try to solve Ax=b. Here" }{TEXT 204 0 "" }}{PARA 203 "" 0 "" {TEXT 204 76 "A is a Matrix, n is \+ the number of times you iterate and v is a start vector." }{TEXT 204 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 21 "Jac := proc(A,b, v,n) " }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 32 "\n local Diag,R, w,j,newb,T;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 44 "\n Diag := DiagonalMatrix(Diagonal(A));" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 30 "\n R:=MatrixAdd(A,-Diag);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 57 "\n T := MatrixMatrixMultiply(MatrixInverse(Diag),R);" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 60 "\n newb := MatrixVectorM ultiply(MatrixInverse(Diag),b);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 13 "\n w:=v;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 28 "\n \+ for j from 1 to n do" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 54 "\n \+ w:=VectorAdd(-MatrixVectorMultiply(T,w),newb);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 13 "\n od:" }{MPLTEXT 1 202 0 "" }}{PARA 202 "> " 0 "" {MPLTEXT 1 0 9 " w;" }{MPLTEXT 1 0 0 "" }}{PARA 202 "> " 0 "" {MPLTEXT 1 0 11 " end proc;" }{MPLTEXT 1 0 0 "" }}{PARA 201 " " 1 "" {XPPMATH 20 "6#>I$JacG6\"f*6&I\"AGF%I\"bGF%I\"vGF%I\"nGF%6(I%Di agGF%I\"RGF%I\"wGF%I\"jGF%I%newbGF%I\"TGF%F%F%C)>8$-_I.LinearAlgebraG6 $I*protectedGF:I(_syslibGF%I/DiagonalMatrixGF%6#-_F8I)DiagonalGF%6#9$> 8%-_F8I*MatrixAddGF%6$FB,$F5!\"\">8)-_F8I5MatrixMatrixMultiplyGF%6$-_F 8I.MatrixInverseGF%6#F5FD>8(-_F8I5MatrixVectorMultiplyGF%6$FQ9%>8&9&?( 8'\"\"\"F[o9'I%trueGF:>Fgn-_F8I*VectorAddGF%6$,$-FX6$FLFgnFJFVFgnF%F%F %" }{TEXT 203 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" } }}{EXCHG {PARA 203 "" 0 "" {TEXT 204 75 "The following gives you the e ntries on the diagonal and below of a matrix A" }{TEXT 204 0 "" }}} {EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 29 "Lower := proc(A) local i ,j,L;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 33 "\n L:=Matrix(ColumnDi mension(A));" }{MPLTEXT 1 202 0 "" }}{PARA 202 "> " 0 "" {MPLTEXT 1 0 39 " for i from 1 to ColumnDimension(A) do" }{MPLTEXT 1 0 0 "" }} {PARA 202 "> " 0 "" {MPLTEXT 1 0 22 " for j from 1 to i do" } {MPLTEXT 1 0 0 "" }}{PARA 202 "> " 0 "" {MPLTEXT 1 0 17 " L[i,j]:=A[i ,j];" }{MPLTEXT 1 0 0 "" }}{PARA 202 "> " 0 "" {MPLTEXT 1 0 5 " od:" }{MPLTEXT 1 0 0 "" }}{PARA 202 "> " 0 "" {MPLTEXT 1 0 5 " od:" } {MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 13 "\n return(L);" }{MPLTEXT 1 0 0 "" }}{PARA 202 "> " 0 "" {MPLTEXT 1 0 9 "end proc;" }{MPLTEXT 1 0 0 "" } }{PARA 201 "" 1 "" {XPPMATH 20 "6#>I&LowerG6\"f*6#I\"AGF%6%I\"iGF%I\"j GF%I\"LGF%F%F%C%>8&-I'MatrixG6$I*protectedGF3I(_syslibGF%6#-_I.LinearA lgebraGF2I0ColumnDimensionGF%6#9$?(8$\"\"\"F>F6I%trueGF3?(8%F>F>F=F?>& F/6$F=FA&F;FDOF/F%F%F%" }{TEXT 203 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 1 " " }{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 " " {MPLTEXT 1 202 29 "Upper := proc(A) local i,j,U;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 33 "\n U:=Matrix(ColumnDimension(A));" }{MPLTEXT 1 202 0 "" }}{PARA 202 "> " 0 "" {MPLTEXT 1 0 39 " for i from 1 to Co lumnDimension(A) do" }{MPLTEXT 1 0 0 "" }}{PARA 202 "> " 0 "" {MPLTEXT 1 0 38 " for j from i+1 to RowDimension(A) do" }{MPLTEXT 1 0 0 "" }}{PARA 202 "> " 0 "" {MPLTEXT 1 0 16 " U[i,j]:=A[i,j];" } {MPLTEXT 1 0 0 "" }}{PARA 202 "> " 0 "" {MPLTEXT 1 0 5 " od:" } {MPLTEXT 1 0 0 "" }}{PARA 202 "> " 0 "" {MPLTEXT 1 0 5 " od:" } {MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 13 "\n return(U);" }{MPLTEXT 1 0 0 "" }}{PARA 202 "> " 0 "" {MPLTEXT 1 0 9 "end proc;" }{MPLTEXT 1 0 0 "" } }{PARA 201 "" 1 "" {XPPMATH 20 "6#>I&UpperG6\"f*6#I\"AGF%6%I\"iGF%I\"j GF%I\"UGF%F%F%C%>8&-I'MatrixG6$I*protectedGF3I(_syslibGF%6#-_I.LinearA lgebraGF2I0ColumnDimensionGF%6#9$?(8$\"\"\"F>F6I%trueGF3?(8%,&F=F>F>F> F>-_F8I-RowDimensionGF%F:F?>&F/6$F=FA&F;FHOF/F%F%F%" }{TEXT 203 0 "" } }}{EXCHG {PARA 203 "" 0 "" {TEXT 204 82 "The following uses the Gauss- Seidel method to iteratively try to solve Ax=b. Here" }{TEXT 204 0 "" }}{PARA 203 "" 0 "" {TEXT 204 76 "A is a Matrix, n is the number of t imes you iterate and v is a start vector." }{TEXT 204 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 20 "GS := proc(A,b,v,n) " } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 38 "\n local w,j,newb,T, B, \+ L,U,Diag;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 44 "\n Diag := D iagonalMatrix(Diagonal(A));" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 30 " \n B:=MatrixAdd(A,-Diag);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 20 "\n L:=Lower(B);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 29 "\n U := MatrixAdd(B,-L);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 70 "\n T := MatrixMatrixMultiply(MatrixInverse(MatrixAdd(L,Diag)),U );" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 73 "\n newb := MatrixVe ctorMultiply(MatrixInverse(MatrixAdd(L,Diag)),b);" }{MPLTEXT 1 202 0 " " }{MPLTEXT 1 202 13 "\n w:=v;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 28 "\n for j from 1 to n do" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 54 "\n w:=VectorAdd(-MatrixVectorMultiply(T,w),ne wb);" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 13 "\n od:" } {MPLTEXT 1 202 0 "" }}{PARA 202 "> " 0 "" {MPLTEXT 1 0 9 " w;" } {MPLTEXT 1 0 0 "" }}{PARA 202 "> " 0 "" {MPLTEXT 1 0 11 " end proc;" }{MPLTEXT 1 0 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#>I#GSG6\"f*6&I\" AGF%I\"bGF%I\"vGF%I\"nGF%6*I\"wGF%I\"jGF%I%newbGF%I\"TGF%I\"BGF%I\"LGF %I\"UGF%I%DiagGF%F%F%C+>8+-_I.LinearAlgebraG6$I*protectedGF8(-_F:I*MatrixAddGF%6$FD, $F7!\"\">8)-I&LowerGF%6#FF>8*-FH6$FF,$FNFL>8'-_F:I5MatrixMatrixMultipl yGF%6$-_F:I.MatrixInverseGF%6#-FH6$FNF7FS>8&-_F:I5MatrixVectorMultiply GF%6$Fgn9%>8$9&?(8%\"\"\"Fio9'I%trueGF<>Feo-_F:I*VectorAddGF%6$,$-F`o6 $FXFeoFLF^oFeoF%F%F%" }{TEXT 203 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 80 "v :=;" }{MPLTEXT 1 202 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#>I \"vG6\"-I'RTABLEGF%6%\"'[+Q-I'MATRIXGF%6#7%7#$\"+\"p'>uU!#57#$\"+Lp56K F17#$\"+P2LOMF1&I'VectorG6$I*protectedGF;I(_syslibGF%6#I'columnGF%" } {TEXT 203 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 20 "ansJ:= Jac(A,b,v,20);" }{MPLTEXT 1 202 0 "" }}{PARA 200 "> " 0 "" {MPLTEXT 1 202 31 "ErrJ:=Norm(VectorAdd(z,-ansJ));" }{MPLTEXT 1 202 0 "" }}{PARA 200 "> " 0 "" {MPLTEXT 1 202 61 "ResidualJ :=Norm(VectorAdd(b,-MatrixV ectorMultiply(A,ansJ)));" }{MPLTEXT 1 202 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#>I%ansJG6\"-I'RTABLEGF%6%\"'7Ld-I'MATRIXGF%6#7%7#$\"3$o ;b9@dx7#!#>7#$\"3W@u5!yg\">`!#=7#$\"3>46#=`)zHQF5&I'VectorG6$I*protect edGFI%ErrJG6\"$\"3'>kw3s$R%=\"!#B" }{TEXT 203 0 "" }} {PARA 201 "" 1 "" {XPPMATH 20 "6#>I*ResidualJG6\"$\"31aYg!fYS**)!#B" } {TEXT 203 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 20 "ansGS: =GS(A,b,v,20);" }{MPLTEXT 1 202 0 "" }}{PARA 200 "> " 0 "" {MPLTEXT 1 202 33 "ErrGS:=Norm(VectorAdd(z,-ansGS));" }{MPLTEXT 1 202 0 "" }} {PARA 200 "> " 0 "" {MPLTEXT 1 202 63 "ResidualGS :=Norm(VectorAdd(b,- MatrixVectorMultiply(A,ansGS)));" }{MPLTEXT 1 202 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#>I&ansGSG6\"-I'RTABLEGF%6%\"'#Rt&-I'MATRIXGF%6#7%7 #$\"3S&3oWdfw7#!#>7#$\"3c6-`!#=7#$\"3GaD/MsyHQF5&I'VectorG6$I*p rotectedGFI&ErrGSG6\"$\"3ac^iCIA56!#L" }{TEXT 203 0 "" }} {PARA 201 "" 1 "" {XPPMATH 20 "6#>I+ResidualGSG6\"$\"3;E1])4#*3W%!#L" }{TEXT 203 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 28 "A:= M atrix([ [1.0,2.0,1.0]," }{MPLTEXT 1 202 0 "" }}{PARA 202 "> " 0 "" {MPLTEXT 1 0 28 " [1.0,3.0,1.0]," }{MPLTEXT 1 0 0 "" }} {PARA 202 "> " 0 "" {MPLTEXT 1 0 31 " [1.0,2.0,5.0] ]);" }{MPLTEXT 1 0 0 "" }}{PARA 200 "> " 0 "" {MPLTEXT 1 202 18 "b:= <1.0,2 .0,3.0>;" }{MPLTEXT 1 202 0 "" }}{PARA 200 "> " 0 "" {MPLTEXT 1 202 20 "z:=LinearSolve(A,b);" }{MPLTEXT 1 202 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#>I\"AG6\"-I'RTABLEGF%6%\"';He-I'MATRIXGF%6#7%7%$\"#5!\" \"$\"#?F1F/7%F/$\"#IF1F/7%F/F2$\"#]F1I'MatrixG6$I*protectedGFI\"bG6\"-I'R TABLEGF%6%\"'7Nd-I'MATRIXGF%6#7%7#$\"#5!\"\"7#$\"#?F17#$\"#IF1&I'Vecto rG6$I*protectedGF;I(_syslibGF%6#I'columnGF%" }{TEXT 203 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#>I\"zG6\"-I'RTABLEGF%6%\"'#ft&-I'MATRIXGF%6 #7%7#$!3++++++++:!#<7#$\"\"\"\"\"!7#$\"3++++++++]!#=&I'VectorG6$I*prot ectedGF=I(_syslibGF%6#I'columnGF%" }{TEXT 203 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 44 "ATA := MatrixMatrixMultiply(Transpose (A),A);" }{MPLTEXT 1 202 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#>I$AT AG6\"-I'RTABLEGF%6%\"'_%)f-I'MATRIXGF%6#7%7%$\"\"$\"\"!$\"\"(F1F27%F2$ \"#I(_syslibGF%" } {TEXT 203 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 43 "ATb:= \+ MatrixVectorMultiply(Transpose(A),b);" }{MPLTEXT 1 202 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#>I$ATbG6\"-I'RTABLEGF%6%\"'7Pd-I'MATRIXGF%6 #7%7#$\"\"'\"\"!7#$\"#9F17#$\"#=F1&I'VectorG6$I*protectedGF;I(_syslibG F%6#I'columnGF%" }{TEXT 203 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 26 "ATz:=LinearSolve(ATA,ATb);" }{MPLTEXT 1 202 0 "" }} {PARA 201 "" 1 "" {XPPMATH 20 "6#>I$ATzG6\"-I'RTABLEGF%6%\"'#zt&-I'MAT RIXGF%6#7%7#$!3a2++++++:!#<7#$\"3m-++++++5F17#$\"3W/++++++]!#=&I'Vecto rG6$I*protectedGF " 0 "" {MPLTEXT 1 202 20 "ansJ:=Jac(A,b,v,50);" } {MPLTEXT 1 202 0 "" }}{PARA 200 "> " 0 "" {MPLTEXT 1 202 31 "ErrJ:=Nor m(VectorAdd(z,-ansJ));" }{MPLTEXT 1 202 0 "" }}{PARA 200 "> " 0 "" {MPLTEXT 1 202 61 "ResidualJ :=Norm(VectorAdd(b,-MatrixVectorMultiply( A,ansJ)));" }{MPLTEXT 1 202 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#>I %ansJG6\"-I'RTABLEGF%6%\"'sQd-I'MATRIXGF%6#7%7#$\"3%H`1n>8S1%!#<7#$\"3 MNZfkp!>?$F17#$\"3ETYl24h!H#F1&I'VectorG6$I*protectedGF;I(_syslibGF%6# I'columnGF%" }{TEXT 203 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#>I%Err JG6\"$\"3%H`1n>8Sc&!#<" }{TEXT 203 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#>I*ResidualJG6\"$\"3=@pTm\")3#*=!#;" }{TEXT 203 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 20 "ansGS:=GS(A,b,v,20);" }{MPLTEXT 1 202 0 "" }}{PARA 200 "> " 0 "" {MPLTEXT 1 202 33 "ErrGS:=Norm(VectorAdd(z,-ansGS));" } {MPLTEXT 1 202 0 "" }}{PARA 200 "> " 0 "" {MPLTEXT 1 202 63 "ResidualG S :=Norm(VectorAdd(b,-MatrixVectorMultiply(A,ansGS)));" }{MPLTEXT 1 202 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#>I&ansGSG6\"-I'RTABLEGF%6% \"'_Rd-I'MATRIXGF%6#7%7#$!3QVC\"y,+$*\\\"!#<7#$\"3A&G'G&Qez***!#=7#$\" 3Ws.^\"o;%**\\F5&I'VectorG6$I*protectedGFI&ErrGSG6\"$\"3!yCm b(=#)**p!#@" }{TEXT 203 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#>I+Res idualGSG6\"$\"3AS-^eRFLB!#@" }{TEXT 203 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 20 "ansGS:=GS(A,b,v,50);" }{MPLTEXT 1 202 0 "" }} {PARA 200 "> " 0 "" {MPLTEXT 1 202 33 "ErrGS:=Norm(VectorAdd(z,-ansGS) );" }{MPLTEXT 1 202 0 "" }}{PARA 200 "> " 0 "" {MPLTEXT 1 202 63 "Resi dualGS :=Norm(VectorAdd(b,-MatrixVectorMultiply(A,ansGS)));" } {MPLTEXT 1 202 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#>I&ansGSG6\"-I' RTABLEGF%6%\"'KSd-I'MATRIXGF%6#7%7#$!3'e_\\j******\\\"!#<7#$\"2Oy_$*)* *******F17#$\"3%*Qz&p*******\\!#=&I'VectorG6$I*protectedGFI& ErrGSG6\"$\"3;k#*=XTZ]O!#E" }{TEXT 203 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#>I+ResidualGSG6\"$\"3nCG4j[#o@\"!#E" }{TEXT 203 0 "" }} }{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 24 "ansGS:=GS(ATA,ATb,v,20) ;" }{MPLTEXT 1 202 0 "" }}{PARA 200 "> " 0 "" {MPLTEXT 1 202 35 "ErrGS :=Norm(VectorAdd(ATz,-ansGS));" }{MPLTEXT 1 202 0 "" }}{PARA 200 "> " 0 "" {MPLTEXT 1 202 67 "ResidualGS :=Norm(VectorAdd(ATb,-MatrixVectorM ultiply(ATA,ansGS)));" }{MPLTEXT 1 202 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#>I&ansGSG6\"-I'RTABLEGF%6%\"'7Td-I'MATRIXGF%6#7%7#$!3=8 %>Frw\\b$!#=7#$\"3\"4*G/mdgBfF17#$\"3?oTk._V(H%F1&I'VectorG6$I*protect edGF;I(_syslibGF%6#I'columnGF%" }{TEXT 203 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#>I&ErrGSG6\"$\"3Bm!G(GB]W6!#<" }{TEXT 203 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#>I+ResidualGSG6\"$\"3&*p<^'\\mN#))!#>" } {TEXT 203 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 25 "ansGS: =GS(ATA,ATb,v,200);" }{MPLTEXT 1 202 0 "" }}{PARA 200 "> " 0 "" {MPLTEXT 1 202 35 "ErrGS:=Norm(VectorAdd(ATz,-ansGS));" }{MPLTEXT 1 202 0 "" }}{PARA 200 "> " 0 "" {MPLTEXT 1 202 67 "ResidualGS :=Norm(Ve ctorAdd(ATb,-MatrixVectorMultiply(ATA,ansGS)));" }{MPLTEXT 1 202 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#>I&ansGSG6\"-I'RTABLEGF%6%\"'#>u&-I 'MATRIXGF%6#7%7#$!3c;8O1^W*[\"!#<7#$\"3/G\"G'=kSi**!#=7#$\"3U?6#Ry?N* \\F5&I'VectorG6$I*protectedGFI&ErrGSG6\"$\"3')*4pQO*[b5!#>" }{TEXT 203 0 "" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#>I+ResidualGSG6\"$ \"3HkEC0qAP\")!#@" }{TEXT 203 0 "" }}}{PARA 204 "" 0 "" {TEXT 205 0 "" }}{PARA 204 "" 0 "" {TEXT 205 0 "" }}{PARA 204 "" 0 "" {TEXT -1 0 "" }}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 15 10 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }{RTABLE_HANDLES 551540 379928 379968 380048 573312 57339 2 582916 573512 573592 598452 573712 573792 573872 573952 574032 57411 2 574192 }{RTABLE M7R0 I3RTABLE_SAVE/551540X,%)anythingG6"6"[gl!"%!!!#*"$"$$"#S!""$"#5F)F*F*$"#IF)$"#? 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