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Re: Generalized Eigenvalue Problem
Posted:
Aug 22, 2008 1:37 AM


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



