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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.
Regards,
Ole