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Re: Root finding procedure?

From: Ole Myren R|hne
Subject: Re: Root finding procedure?
Date: Sat, 5 Jul 1997 19:32:45 +0200

On Fri, 4 Jul 1997, Thomas Hoffmann wrote:

> I am looking for octave- or matlab-code, that allows me to find the
> roots of the polynomial of x that results from det(H)=0, where the Hij
> are polynomials in x theirself.
> E.g.: find the roots x for
>        3x-4    2x+9
> det (                 ) = 0
>        -x+22   4x-11

I don't know if this is of any use:

If your Hij polynomials are indeed *first order*, it should be possible
to cast your problem in the form of a generalized eigenvalue problem:

        Ay = x By (B=1 gives simple eigenvalue problem)

If B has an inverse C (CB = 1) this is equivalent to the simple
eigenvalue problem

       CAy = x y

In your simple example,

    (-4   9)
A = (22 -11)

    ( 3   2)
B =-(-1   4)

AFAIK, EISPACK and/or LAPACK have routines that solve the generalized
eigenvalue problem. I don't know if any such routine is interfaced to
octave, but writing the glue code should be easy.

If your Hij are not *first order*, it seems to me that the trick could
still work, but the matrix dimension will increase.



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