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Topic: Generalized Eigenvalue Problem
Replies: 5   Last Post: Dec 12, 2012 1:58 PM

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Greg Heath

Posts: 5,965
Registered: 12/7/04
Re: Generalized Eigenvalue Problem
Posted: Aug 22, 2008 1:37 AM
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On Aug 19, 2:28 pm, "Reza " <bag...@gmail.com> wrote:
> I'm trying to find smallest eigenvalue of A & B matrices by
> solving (Ax=LBx) using eig(A,B) command. The only special
> thing about my problem is that elements of A have a large
> range from -10^13 to 10^13. It seems that Matlab procedure
> is not so efficient for the problems of this type. I'm
> pretty sure that it's missing some of the smaller eigenvalues.


You can rescale the problem.

You don't give the range of B, so what follows is rather general:

Any matrix, D can be factored into the form

U = R*V*C

Where R (row multiplier) and C (column multiplier) are
nonsingular diagonal matrices with elements that are
exact powers of 2 and abs(V) <= 1 (or any other power of 2).

For constant L, A = R*D*C, B = E*C, x = C\y

A*x = L*B*x ==> D*y = L*(R\E)*y

Hope this helps.

Greg





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