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Polynomial eigenvalue problem

returns
the eigenvalues for the polynomial eigenvalue problem of
degree `e`

= polyeig(`A0,A1,...,Ap`

)`p`

.

`[`

also returns
matrix `X`

,`e`

] =
polyeig(`A0,A1,...,Ap`

)`X`

, of size `n`

-by-`n*p`

,
whose columns are the eigenvectors.

`[`

additionally
returns vector `X`

,`e`

,`s`

]
= polyeig(`A0,A1,...,Ap`

)`s`

, of length `p*n`

,
containing condition numbers for the eigenvalues. At least one of `A0`

and `Ap`

must
be nonsingular. Large condition numbers imply that the problem is
close to a problem with repeated eigenvalues.

[1] Dedieu, Jean-Pierre, and Francoise Tisseur.
"Perturbation
theory for homogeneous polynomial eigenvalue problems." *Linear
Algebra Appl.* Vol. 358, 2003, pp. 71–94.

[2] Tisseur, Francoise, and Karl Meerbergen.
"The
quadratic eigenvalue problem." *SIAM Rev.* Vol.
43, Number 2, 2001, pp. 235–286.

[3] Francoise Tisseur. "Backward error
and condition of polynomial eigenvalue problems." *Linear
Algebra Appl.* Vol. 309, 2000, pp. 339–361.

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