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Solving linear equations with symbolic RHS

• To: mathgroup at smc.vnet.net
• Subject: [mg30141] Solving linear equations with symbolic RHS
• From: "Tony MacKenzie" <mackenzi at usq.edu.au>
• Date: Tue, 31 Jul 2001 04:27:13 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Once again I would like to thank everyone who helped with my last post. This
question is more general and therefore probably much more difficult to
answer.

I am trying to solve linear equations of the form  A.x=b.  A is a completely
numeric matrix but b is a symbolic vector. I have tried Solve and
LUDecomposition but neither of these seem to work very well when b is a
symbolic vector.  What has worked the best for me is to invert the matrix A
(There is no problem with ill-conditioning) and to multiply by the symbolic
vector b.  However, what slows this process down is when I expand the
result.

Ainv=Inverse[N[A,16]];
soln=Ainv.N[b,16];
Expand[soln];  (This last steps slows down dramatically as the size of the
problem increases).

Each element of the symbolic solution vector may have a large number of
terms.

I realise this question I am posting is quite vague but if anyone has any
ideas it would be greatly appreciated.

Tony MacKenzie