Linearizations of Matrix Polynomials in Bernstein Bases

Mackey, D. Steven and Perovic, Vasilije (2014) Linearizations of Matrix Polynomials in Bernstein Bases. [MIMS Preprint]

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Abstract

We discuss matrix polynomials expressed in a Bernstein basis, and the associated polynomial eigenvalue problems. Using Mobius transformations of matrix polynomials, large new families of strong linearizations are generated. Matrix polynomials that are structured with respect to a Bernstein basis, together with their associated spectral symmetries, are also investigated. The results in this paper apply equally well to scalar polynomials, and include the development of new companion pencils for polynomials expressed in a Bernstein basis.

Item Type: MIMS Preprint
Uncontrolled Keywords: matrix polynomial, Bernstein polynomials, Mobius transformation, eigenvalue, spectral symmetry, companion pencil, strong linearization, structured linearization
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Dr. D. Steven Mackey
Date Deposited: 01 Jul 2015
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2330

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