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Re: Generalized Eigenvalue Problem
Posted:
Aug 22, 2008 2:08 PM


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 QZfactorization, 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 > > <c4db3545ba524604b0038be607846...@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 



