Weighted restarting method in the weighted Arnoldi algorithm for computing the eigenvalues of a nonsymmetric matrix

In this paper, we present a new algorithm, which is called weighted restarting algorithm for computing the eigenvalues of a nonsymmetric matrix. It has been applied to the weighted Arnoldi method, developed by [A. Essai, Weighted FOM and GMRES for solving nonsymmetric linear systems, Numer. Algorithm 18 (1998) 277–292]. The implementation of the algorithm has been tested by numerical examples, the results show that the algorithm converges fast and works with high accuracy.