Re: Quadratic Eigen value problems?

[Fumihiro CHIBA]

Hi,  S!)ren

consider the following problem:
lambda^2 A u + lambda B  u + C u == 0,
where 0 is zero vector; lambda is unknown scalar; 
u is unknwon vector; A,B and C are given matrices.

introduce auxiliary vector v as follows.
v= lambda u.
the problem is transformed to:
lambda A v + lambda B u == -C u,
lambda u == v.

matrix representation of this problem is
lambda [[B A];[I 0]] * [u;v] == [-C; I][u:v],
where I is unit matrix.
this is a generalized eigenvalue problem.
octave function qz can be applied to this problem.

Reference: 
SIAM Review Vol. 43 No. 2 pp. 235--286, 
F. Tisseur and K. Meerbergen, "The quadratic eigenvalue problem"

2007-07-12, 15:52 JST,  "S!)ren Hauberg" <address@hidden> wrote:
>Hi,
>   I just stumbled upon a cool algorithm that I'd like to try out. It 
>requires that I solve a Quadratic Eigen Value problem. The article 
>mentions that I can do this in Matlab using the 'polyeig' function. 
>Unfortunately it seems that Octave doesn't have this function :-(
>   Does anybody know how to solve such problems with Octave?
>
>S!)ren