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Re: Generalized eigenvalue problem

From: Dirk Laurie
Subject: Re: Generalized eigenvalue problem
Date: Fri, 19 Jun 1998 12:18:53 +0200 (SAT)

Thomas Hoffmann wrote:
> Does anybody of you know a way to solve a generalized eigenvalue problem with
> Octave?
>  It is, e.g. , of the form   M A = k N A,
>  M and N are known and I want to compute the eigenvalues k and the
>  eigenvectors A.
That equation holds when k is a scalar and A is a vector.
The matrix equation is   M A = N A K  where A is a matrix and K is
a diagonal matrix.

If N is non-singular, then   
does what you want.

If N is singular, then the original problem may be ill-behaved in
various ways.

It is true that there are sophisticated algorithms that deliver
better efficiency and accuracy than the one-liner above; in particular,
if A and N are symmetric and N is positive definite.  They are not as 
far as I know available in Octave.  You can look for Fortran sources
under the name 'QZ algorithm".


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