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

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Novak

Posts: 1
Registered: 2/19/09
Re: Generalized Eigenvalue Problem
Posted: Feb 19, 2009 4:39 PM
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Hi Greg,

Can you please clarify:

If the problem
[evec,eval] = eig(A,B)
can be recast as
[evec,eval] = eig(D,(R\E))
then how does one compute D, R, E?

> A = R*D*C
What sort of decomposition is this?

> B = E*C
I presume that E can be obtained from B and C
E = B*C\I

cheers,
Novak.

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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