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Ill-conditioned linear system

• To: mathgroup at smc.vnet.net
• Subject: [mg104302] Ill-conditioned linear system
• From: guerom00 <guerom00 at gmail.com>
• Date: Tue, 27 Oct 2009 04:57:13 -0500 (EST)

Hello everyone,

I try to solve an ill conditioned linear system to no avail for the
moment. When I say ill conditioned, the condition number for my matrix
can easily reach 10*^40, 10*^50. I see that Mathematica gives up and
gives me rubbish around a condition number of 10*^20.

I tried all sorts of preconditioner but nothing works. I also tried
all sorts of options to the LinearSolve[] fucntion.

If my linear system is Ax=b, my matrix A is of the form (MatrixExp
[M] . C). The matrix C is well conditioned. But the eigenvalues of the
matrix M can easily spread from minus a few hundred to plus a few
hundred. Taking the exponential is then dramatic...

Any ideas would be much appreciated.
TIA