Heike, Fassbender and Javier, Perez Alvaro and Nikta, Shayanfar
(2015)
*A sparse linearization for Hermite interpolation matrix
polynomials.*
[MIMS Preprint]

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## Abstract

The polynomial eigenvalue problem for Hermite interpolation matrix polynomials is discussed. The standard approach to solve a polynomial eigenvalue problem is via linearization. In this work we introduce a new linearization for Hermite interpolation matrix polynomials expressed in the first barycentric form that is more sparse than the ones known so far. In addition, we show that this linearization is a strong linearization, and that eigenvectors of the polynomial and those of the linearization are related in simple ways. Finally, the backward errors of computed eigenpairs of the original and the linearized problem are compared as well as eigenvalue condition numbers.

Item Type: | MIMS Preprint |
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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: | Javier Perez Alvaro |

Date Deposited: | 12 Nov 2015 |

Last Modified: | 08 Nov 2017 18:18 |

URI: | http://eprints.maths.manchester.ac.uk/id/eprint/2405 |

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