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

Madhusudan Singh wrote: > 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

**Follow-Ups**:**sparse matrix question***From:*Ted Sariyski <tsariysk@craft-tech.com>