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.