Note on Finding an Optimal Deflation for Quadratic Matrix Polynomials

Note on Finding an Optimal Deflation for Quadratic Matrix Polynomials

Year:    2021

Author:    Xin Liang

CSIAM Transactions on Applied Mathematics, Vol. 2 (2021), Iss. 2 : pp. 336–356

Abstract

This paper is concerned with the way to find an optimal deflation for the eigenvalue problem associated with quadratic matrix polynomials. This work is a response of the work by Tisseur et al., $Linear$ $Algebra$ $Appl$., $435:464-479, 2011$, and solves one of open problems raised by them. We build an equivalent unconstrained optimization problem on eigenvalues of a hyperbolic quadratic matrix polynomial of order 2, and develop a technique that transforms the quadratic matrix polynomial to an equivalent one that is easy to solve. Numerical tests are given to illustrate several properties of the problem.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/csiam-am.2021.nla.05

CSIAM Transactions on Applied Mathematics, Vol. 2 (2021), Iss. 2 : pp. 336–356

Published online:    2021-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    21

Keywords:    deflation quadratic matrix polynomials hyperbolic eigenvalue optimization.

Author Details

Xin Liang