Re: Numerical Determinants

• To: mathgroup at smc.vnet.net
• Subject: [mg13178] Re: Numerical Determinants
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Mon, 13 Jul 1998 07:42:26 -0400
• Organization: University of Western Australia
• References: <6n4o6m\$nin@smc.vnet.net> <6n9m67\$9hq@smc.vnet.net> <6nnb0k\$5em@smc.vnet.net> <6nsj1a\$f3t@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Rod Pinna wrote:

I tried responding to rpinna at civil.uwa.edu.au but it bounced and you
don't seem to be listed on the University of Western Australia CWIS?

> Which probably indicates that I should have listened better in  first
> year mathematics :)
>
> That was the idea I was following, but since it hadn't been  mentioned
> as a method in a couple of the texts I consulted, I  thought that there
> might be something I was missing. Basically,  everything talks about
> inverting the B matrix, but then doesn't  mention what to do in B in
> singular. As the above *seemed*  obvious, I thought that there might be
> a reason it wasn't  mentioned.

Daniel Lichtblau <danl at wolfram.com> pointed out that numeric stability
can be a problem.  However, since I recall that your matrices are not
large, you can use arbitrary (or fixed) precision to track the
stability.

Dan also mentioned that by taking the LUDecomposition one can get a good
estimate of the matrix condition number, which in turn gives an
indication of how good a result might be obtained by using the inverse
in this way. If you can guarantee that condition numbers are small for
the class of matrix you use then you might even be fine with machine
arithmetic.

Cheers,
Paul

____________________________________________________________________
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia            Nedlands WA  6907
mailto:paul at physics.uwa.edu.au  AUSTRALIA
http://www.pd.uwa.edu.au/~paul

God IS a weakly left-handed dice player
____________________________________________________________________

```

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