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Polynomial eigenvalue problem

• To: mathgroup at smc.vnet.net
• Subject: [mg58699] Polynomial eigenvalue problem
• From: "Alan" <info at optioncity.REMOVETHIS.net>
• Date: Fri, 15 Jul 2005 03:02:14 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Does anyone know a Mathematica solution
for the polynomial eigenvalue problem (PEP)?

The PEP problem of order p . N is:
Find the eigenvalues lambda, and eigenvectors v (each an N-vector) that 
solve

(A_0 + lambda A_1 + lambda^2 A_2 + ... + lambda^p A_p) x = 0,

where:
p is a given integer,
each coefficients A_i is a given N x N (real or complex) square matrix.

There are p . N solution pairs (lambda, x) if the problem is not ill-posed.
If both A_0 and A_p are singular the problem is potentially ill-posed.

Thanks for any help,
alan

 

• Follow-Ups:
  • Re: Polynomial eigenvalue problem
    • From: "Carl K. Woll" <carl@woll2woll.com>