Note on Finding an Optimal Deflation for Quadratic Matrix Polynomials (CSIAM Transactions on Applied Mathematics, 2021)
This paper is concerned with the way to find an optimal deflation for theeigenvalue 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 solvesone 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 propertiesof the problem.
Keywords: deflation; quadratic matrix polynomials; hyperbolic; eigenvalue optimization.