Re: Eigensystems

• To: mathgroup at smc.vnet.net
• Subject: [mg18940] Re: Eigensystems
• From: Rod Pinna <rpinna at civil.uwa.edu.au>
• Date: Fri, 30 Jul 1999 01:33:37 -0400
• Organization: The University of Western Australia
• References: <7nef9i\$238@smc.vnet.net> <7nlote\$bb3@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```adam.smith at hillsdale.edu writes:

> Perhaps I do not fully understand the question.  But assuming that
> lambda is a scalar constant and both A and B are square n-by-n
> matrices.  Then the following solves for the eigensystem
>
> Eigensystem[ Inverse[B].A ]
>
> returning the eigenvalues and associated eigenvectors.  Any
> misunderstanding may lie in what you mean by "efficient".  Some quick
> tests show that as long as A and B are assigned numeric values and not
> simple symbolic letters, Mathematica returns a solution very rapidly.
> However, if you what a complete symbolic answer things get very messy
> and can take a considerable amount of time and require a great deal of
> memory.  I solved a 2-by-2 system rather quickly, but the output answer
> was very long.
>

The above works very well with numeric systems, I my experience.
It is also reasonably OK with a small number of symbolic variables
for small matricies. However, I've found that the solution time
is very different for different amchines, for symbolic values.

For example, for the type of system I usually solve, (3x3, a few
symbolic values) a P200, running linux takes about 45 mins, while
a 466 DEC alpha does it in about 3 seconds. The increase in speed
seems to be out of proportion to the increase in processor speed.

BTW, if you have symbolic values, you'll need quite a bit of memory.

And if anyone has any ideads about something more efficient than the
above for symbolic matricies, I'd be very happy to hear it.

Regards,
Rod Pinna

```

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