       Re: Slow LinearSolve.

• To: mathgroup at smc.vnet.net
• Subject: [mg49664] Re: [mg49657] Slow LinearSolve.
• From: "Christos Argyropoulos MD" <chrisarg at medscape.com>
• Date: Tue, 27 Jul 2004 07:00:42 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Hi ,
Try entering the problem as LinearSolve[N[A],N[b]].
The reason it takes for ever, is that your matrices consist
of "exact" numbers i.e. e, I, Pi and Mathematica tries to give you an
exact i.e. symbolic result. That will take for ever since the
symbolic solutions of linear systems is computationally expensive. If
the matrices with N[]; then they will converted to Floating Point and
evaluated numerically FAST as the following shows (Math4.2 XP Pro
Intel at 3.0GHz HT 4 GB DDR)
In:=
Timing[Table[LinearSolve[N[A],N[b]],{1000}];]

Out=
{0.187 Second,Null}
\!\({\(\(0.0744635081595152`\)\(\[InvisibleSpace]\)\) + \
3.7253195763747384`*^-14\ \[ImaginaryI], \(\(0.42971490576141286`\)\(\
\[InvisibleSpace]\)\) - 2.4999986347577774`*^-13\ \[ImaginaryI], \
\(-0.07819866153696708`\) + 8.649608688391904`*^-13\ \[ImaginaryI], \
\(\(0.8882136952400588`\)\(\[InvisibleSpace]\)\) -
2.0302351108874434`*^-12\ \
\[ImaginaryI], \(-0.7103217579953505`\) + 3.571291726971529`*^-12\ \
\[ImaginaryI], \(\(1.5245842254651043`\)\(\[InvisibleSpace]\)\) - \
4.937329408163937`*^-12\ \[ImaginaryI], \(-1.1153191765977668`\) + \
5.485925299100747`*^-12\ \[ImaginaryI], \(\(1.5245842254651498`\)\(\
\[InvisibleSpace]\)\) - 4.932307492121202`*^-12\ \[ImaginaryI], \
\(-0.7103217579954203`\) + 3.562747427805768`*^-12\ \[ImaginaryI], \
\(\(0.8882136952401251`\)\(\[InvisibleSpace]\)\) -
2.0202080839356457`*^-12\ \
\[ImaginaryI], \(-0.07819866153701173`\) + 8.564310183614438`*^-13\ \
\[ImaginaryI], \(\(0.4297149057614334`\)\(\[InvisibleSpace]\)\) - \
2.450344072611743`*^-13\ \[ImaginaryI], \(\(0.0744635081595099`\)\(\
\[InvisibleSpace]\)\) + 3.602152386151295`*^-14\ \[ImaginaryI]}\)

The "other" product probably cannot do symbolic AND numerical stuff.
So stick with Mathematica
Christos Argyropoulos MD MSc
Patras Greeece

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