A variant of second-order Arnoldi method for solving the quadratic eigenvalue problem

摘要

In this paper, we give a variant of second-order Krylov subspace R-n(A, B; u) based on a pair of square matrices A and B and a vector u, which is a modification of second-order Krylov subspace presented by Bai and Su [SIAM J. Matrix Anal. Appl., 26(2005) 640-659]. Then we can compute an orthonormal basis of R-n(A,B; u) by using second-order Arnoldi procedure. By applying the standard Rayleigh-Ritz orthogonal projection technique, a variant of second-order Arnoldi method (VSOAR) for solving large-scale quadratic eigenvalue problems (QEPs) has been presented. Finally, numerical experiments are given to show the efficiency of the new method.