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William
Posts:
15
Registered:
4/23/08
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Re: Generalized Eigenvalue Problem
Posted:
Aug 22, 2008 4:10 AM
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What is this method called? I'm struggling with a similar
problem, Ax=lBx, where B has a huge range.
When performing a QZ-factorization, I get one value of
beta=0, which gives me infinite eigenvalues...
Greg Heath <heath@alumni.brown.edu> wrote in message
<c4db3545-ba52-4604-b003-8be607846484@a70g2000hsh.googlegroups.com>...
> On Aug 19, 2:28=A0pm, "Reza " <bag...@gmail.com> wrote:
> > I'm trying to find smallest eigenvalue of A & B matrices by
> > solving (Ax=3DLBx) 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 =3D 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) <=3D 1 (or any other power of 2).
>
> For constant L, A =3D R*D*C, B =3D E*C, x =3D C\y
>
> A*x =3D L*B*x =3D=3D> D*y =3D L*(R\E)*y
>
> Hope this helps.
>
> Greg
>
>
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