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 |
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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: | https://eprints.maths.manchester.ac.uk/id/eprint/2560 |

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