Re: Fast solution to very small eigenvalue problem
From: K. Doniger (k.doniger_at_ieee.org)
Date: 06/25/04
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Date: Fri, 25 Jun 2004 02:56:06 GMT
Mark Mackey wrote:
> Hi all.
>
> I need to find the eigenvector corresponding to the largest eigenvalue
> of a 4x4 matrix very quickly (because I'm doing it on hundreds of
> thousands of 4x4 matrices). The current code I'm maintaining has a
> simple Jacobi solver, which is (a) slow (it only does 30K matrices/s on
> my PC), and (b) probably overkill, as it returns all of the
> eigenvectors. I've vaguely looked at LAPACK etc, but those routines are
> AFAIK optimised for good performance on large matrices, not small ones.
>
> Does anyone have any suggestions as to the most efficient way to solve
> this problem? Extreme accuracy is not required. 4x4 is probably small
> enough that there's an analytic solution :).
>
If this derives from a physical problem, perhaps you can use Rayleigh's
variational principle.
- Ken
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