(untitled) (CSIAM Transactions on Applied Mathematics, 2021)
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.