A new method for calculating eigenpairs of a non-symmetric matrix

In this paper, we present a new algorithm, which called PSO restarted Arnoldi algorithm (PSO-RA) for calculating eigenpairs of a non-symmetric matrix. In most of the restarting methods the basic idea is a selection of the best initial eigenvector, but our aim is to improve the initial eigenvectors in each iteration of the restarting method. Numerical examples are used to show the good numerical properties.