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2015.98: A sparse linearization for Hermite interpolation matrix polynomials

2015.98: Fassbender Heike, Perez Alvaro Javier and Shayanfar Nikta (2015) A sparse linearization for Hermite interpolation matrix polynomials.

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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
Subjects:MSC 2000 > 15 Linear and multilinear algebra; matrix theory
MSC 2000 > 65 Numerical analysis
MIMS number:2015.98
Deposited By:Javier Perez Alvaro
Deposited On:12 November 2015

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