The Mathematical Institute, University of Oxford, Eprints Archive

Vector spaces of linearizations for matrix polynomials: A bivariate polynomial approach

Townsend, Alex and Noferini, Vanni and Nakatsukasa, Yuji (2012) Vector spaces of linearizations for matrix polynomials: A bivariate polynomial approach. Technical Report. SIMAX. (Submitted)

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Abstract

We revisit the important paper [D. S. Mackey, N. Mackey, C. Mehl, and V. Mehrmann, SIAM J. Matrix Anal. Appl., 28 (2006), pp. 971-1004] and, by viewing matrices as coefficients for bivariate polynomials, we provide concise proofs for key properties of linearizations for matrix polynomials. We also show that every pencil in the double ansatz space is intrinsically connected to a Bézout matrix, which we use to prove the eigenvalue exclusion theorem. In addition our exposition allows for any degree-graded basis, the monomials being a special case. MATLAB code is given to construct the pencils in the double ansatz space for matrix polynomials expressed in any orthogonal basis.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Linear and multilinear algebra; matrix theory
H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1638
Deposited By: Lotti Ekert
Deposited On:20 Dec 2012 08:39
Last Modified:29 May 2015 19:19

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