       Re: Wierd problems with Mathematica - inversion of a 12x12 matrix

• To: mathgroup at smc.vnet.net
• Subject: [mg56090] Re: Wierd problems with Mathematica - inversion of a 12x12 matrix
• From: David Bailey <dave at Remove_Thisdbailey.co.uk>
• Date: Fri, 15 Apr 2005 04:47:31 -0400 (EDT)
• References: <d3lrsq\$sef\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

> Hi
>
> I am solving a problem using f95 that involves solving a 12x12 coupled
> linear system. I have written out the matrix A (A x = f), and instead of
> calculating the inverse repeatedly for different values of the input
> parameters, I am trying to calculate the symbolic inverse of the matrix,
> post multiply it with the RHS and code the resulting 12 equations for x_i
> into fortran.
>
> I believe this is the sensible way to do it, since this system needs to be
> solved lots of times (its part of a half-infinite integral) and inverting
> such a system numerically would not only be time consuming, but also
> obscure possible stability problems.
>
> Now, I am using Mathematica 5.1 (multiprocessor Sun machine) to do it, but
> the inverse has been running for the past 40 minutes without any result. A
> prior attempt to run it with Mathematica 4.1 (single processor Pentium M
> Linux machine) resulted in an aborted process.
>
> Out of a hunch, I just exported the notebook to text, and used "math" (the
> text version of Mathematica) to run it through. Less that two minutes
> later, I had an answer. The problem is that the answer (in nohup.out) is so
> ill formatted (I used MatrixForm with FullSimplify) that it is impossible to
> make sense of.
>
> OTOH, the graphical Notebook is still chugging away. Has anyone seen this
> odd behaviour before ?
>
> Thanks.
>
This is only a guess (because you have not supplied any actual code),
but make sure your matrix only contains real numbers before you attempt
to invert it - use N if necessary. A simple example will show you what
can happen otherwise:

{{1, 2, 3}, {7, 1, 7}, {9, 4, 7}} // Inverse

Mathematica tries to perform the inversion by exact rational arithmetic,
and that gets a bit expensive with a 12x12!

David Bailey
dbaileyconsultancy.co.uk

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