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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: 5,923
Registered: 12/7/04
Re: Generalized Eigenvalue Problem
Posted: Aug 22, 2008 2:08 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Aug 22, 4:10 am, "William " <wilstr...@stud.hive.no> wrote:
> What is this method called? I'm struggling with a similar
> problem, Ax=lBx, where B has a huge range.


I saw it in a numerical analysis book about 25 or 30 years ago. I
assume it is a well known technique for
rescaling matrix problems.

> When performing a QZ-factorization, I get one value of
> beta=0, which gives me infinite eigenvalues...


I am not familiar with QZ and have no idea what beta is.

Please explain.

Greg

> Greg Heath <he...@alumni.brown.edu> wrote in message
>
> <c4db3545-ba52-4604-b003-8be607846...@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- Hide quoted text -
>
> - Show quoted text -





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