A modified second-order Arnoldi method for solving the quadratic eigenvalue problems

Based on a pair of square matrices A and B and a vector u, a modified second-order Krylov subspace Rn(A,B;u) is first defined, which generalizes the standard Krylov subspace and the second-order Krylov subspace proposed by Bai and Su (2005). Then a modified second-order Arnoldi procedure for generating an orthonormal basis of Rn(A,B;u) has been presented. By applying the standard Rayleigh-Ritz orthogonal projection technique, a modified second-order Arnoldi method (MSOAR) for solving a large-scale quadratic eigenvalue problems (QEP) has been proposed. Finally, numerical experiments are given to show the efficiency of the new method.