On a class of alternating coefficient matrices quadratic eigenvalue problem

摘要

In this paper, we consider a class of alternating coefficient matrices quadratic eigenvalue problem (AQEP) appearing in a wide range of applications. At first, the AQEP is reformulated as a generalized eigenvalue problem (GEP) by applying Tisseur's linearization technique. Then we point out a property about skew-symmetric tridiagonal matrix eigenvalue problem. Consequently, we give that the corresponding GEP can be solved by applying the Cholesky-QL algorithm or Lanczos algorithm without complex arithmetic. The structured backward error for QEP would be discussed because of the special structure of the polynomial eigenvalue problems. We develop structured condition number, the upper bound and the lower bound are given. Some computational experiments and some concluding remarks are provided.