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MathGroup Archive 2007

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Dependence of precision on execution speed of Inverse

  • To: mathgroup at smc.vnet.net
  • Subject: [mg81568] Dependence of precision on execution speed of Inverse
  • From: "Andrew Moylan" <andrew.j.moylan at gmail.com>
  • Date: Fri, 28 Sep 2007 02:06:13 -0400 (EDT)

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.





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