TY - JOUR T1 - Note on Finding an Optimal Deflation for Quadratic Matrix Polynomials AU - Liang , Xin JO - CSIAM Transactions on Applied Mathematics VL - 2 SP - 336 EP - 356 PY - 2021 DA - 2021/05 SN - 2 DO - http://doi.org/10.4208/csiam-am.2021.nla.05 UR - https://global-sci.org/intro/article_detail/csiam-am/18888.html KW - deflation, quadratic matrix polynomials, hyperbolic, eigenvalue optimization. AB -

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.