Linearizations of Matrix Polynomials in Newton Bases

Perovic, Vasilije and Mackey, D. Steven (2017) Linearizations of Matrix Polynomials in Newton Bases. [MIMS Preprint]

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Abstract

We discuss matrix polynomials expressed in a Newton basis, and the associated polynomial eigenvalue problems. Properties of the generalized ansatz spaces associated with such polynomials are proved directly by utilizing a novel representation of pencils in these spaces. Also, we show how the family of Fiedler pencils can be adapted to matrix polynomials expressed in a Newton basis. These new Newton-Fiedler pencils are shown to be strong linearizations, and some computational aspects related to them are discussed.

Item Type: MIMS Preprint
Uncontrolled Keywords: matrix polynomial, Newton bases, strong linearization, Newton-Fiedler pencil, ansatz space, updating
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory
MSC 2010, the AMS's Mathematics Subject Classification > 41 Approximations and expansions
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Dr. D. Steven Mackey
Date Deposited: 18 Jul 2017
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2560

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