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MathGroup Archive 2004

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LinearSolve and Matrix inversion

  • To: mathgroup at smc.vnet.net
  • Subject: [mg47881] LinearSolve and Matrix inversion
  • From: "Filipe" <fjsc2 at hotmail.com>
  • Date: Thu, 29 Apr 2004 03:06:22 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

I have reasonably small dense determined systems of symbolic linear
equations ranging from 2x2 to 56x56.
The two fastest ways to solve them seem to be either LinearSolve[A,B] or
Inverse[A].B, with the options Method->CofactorExpansion and
OneStepRowReduction being the fastest methods for this particular set of
equations.

Now, the problem is that when performing the Gaussian elimination needed for
LinearSolve and Inverse, Mathematica doesn't seem to simplify intermediate
results. This means that even at 11x11 I am stuck with a huge answer, which
is unmanageable (it takes up 800+MB and many hours to Simplify to a
relatively 'simple' answer), thus making it impossible to go to the next
step (15x15), for which the complexity growth would be brutal.

Is there a way to override this and force Mathematica to perform
intermediate simplifications? If not, what are the alternatives - short of
having to write my own program for doing this?


Thank you in advance for any help.

ps: Clearly, other CASs are able to do this operation easily, since other
people have done the exact same calculation 12 years ago(!) up to 56x56 with
computers almost 100x slower.


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