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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 256 48 "Numerical \+
Linear Algebra using the NAG libraries" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "with(LinearAlgebra):" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 92 "First, we are going to solve a linear system using hardwa
re floating point arithmetic (IEEE)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "UseHardwareFloats := true:" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 30 "m := 100; n := 100; nrhs := 2;" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"mG\"$+\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"n
G\"$+\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%nrhsG\"\"#" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "M := Matrix(m,n,(i,j)->1/(1+i+j),da
tatype=float);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG-%'RTABLEG6+\"
)O8?B&%&floatG6#\"\")%'MatrixG%,rectangularG%.Fortran_orderG7\"\"\"#;
\"\"\"\"$+\"F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "b := Matr
ix(n,nrhs,(i,j)->i+j,datatype=float);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%\"bG-%'RTABLEG6+\")wCRB&%&floatG6#\"\")%'MatrixG%,rectangularG%.F
ortran_orderG7\"\"\"#;\"\"\"\"$+\";F3F1" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 55 "st:=time():x := LinearSolve(M,b,method='LU');time()-s
t;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG-%'RTABLEG6+\"()=y6&%&floa
tG6#\"\")%'MatrixG%,rectangularG%.Fortran_orderG7\"\"\"#;\"\"\"\"$+\";
F3F1" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"#!*!\"$" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 16 "Norm( M.x - b );" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"3+]PM_hb#=\"!#@" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
107 "The result that we get is not very accurate since M is a Hilbert \+
matrix with a very high condition number: " }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 30 "ConditionNumber(M,'infinity');" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"+1V^UV\"#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 142 "
So, in order to get a better result, we increase the precision to 25 d
igits. Now we need to use arbitrary precision software float arithmeti
c." }}{PARA 0 "" 0 "" {TEXT -1 33 "This is slower but more accurate:" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "UseHardwareFloats := fals
e;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%2UseHardwareFloatsG%&falseG" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "Digits := 25;" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%'DigitsG\"#D" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 49 "M := Matrix(m,n,(i,j)->1/(1+i+j),datatype=float);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG-%'RTABLEG6+\")%o>H#%'sfloatG%'M
atrixG%,rectangularG%.Fortran_orderG7\"\"\"#;\"\"\"\"$+\"F/" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "b := Matrix(n,nrhs,(i,j)->i+
j,datatype=float);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG-%'RTABLEG
6+\");lNB%'sfloatG%'MatrixG%,rectangularG%.Fortran_orderG7\"\"\"#;\"\"
\"\"$+\";F0F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "st:=time()
:x := LinearSolve(M,b,method='LU');time()-st;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"xG-%'RTABLEG6+\")K\"RI#%'sfloatG%'MatrixG%,rectangu
larG%.Fortran_orderG7\"\"\"#;\"\"\"\"$+\";F0F." }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"&L`\"!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
12 "Norm(M.x-b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"$f\"!#5" }}}
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F9AF&
}
{RTABLE 
M6R0
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}
{RTABLE 
M6R0
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