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MathGroup Archive 2007

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Re: Dependence of precision on execution speed of Inverse

  • To: mathgroup at smc.vnet.net
  • Subject: [mg81606] Re: Dependence of precision on execution speed of Inverse
  • From: Andrew Moylan <andrew.j.moylan at gmail.com>
  • Date: Sat, 29 Sep 2007 02:26:33 -0400 (EDT)
  • References: <fdi5li$q8j$1@smc.vnet.net>

On Sep 28, 4:06 pm, "Andrew Moylan" <andrew.j.moy... at gmail.com> wrote:
> m1=RandomReal[1,{50,50}];
> m2=SetPrecision[m1,14];
> Do[Inverse[m1];,{1500}]//Timing
> Do[Inverse[m2];,{10}]//Timing
>
> On my machine, both Timing results are about the same, indicating that
> Inverse (of 50x50 matrices) is about 150 times faster for machine-precision
> numbers than for arbitrary precision numbers (of precision ~14). This factor
> of 150 seems large. Does Mathematica employ an Inverse algorithm that is
> optimised for Mathematica's arbitrary-precision numbers?
>
> Notes:
> * Changing the precision of m2 from 14 to e.g. 17 makes little difference.
> * Calling Developer`FromPackedArray[] on m1 makes little difference.
> * Calling LinearSolve on Inverse yields somewhat different results, but
> still shows a difference in execution time of a factor of order 100.

Corrections of two typos I made:
* In the last sentence, "Calling LinearSolve on Inverse" should read
"Calling LinearSolve instead of Inverse".
* In the subject line, "Dependence of precision on" should read
"Dependence on precision of".



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