A modification on minimum restarting method in the Arnoldi algorithm for computing the eigenvalues of a nonsymmetric matrix

In this paper we intend to modify “min restarting method” presented in [H. Saberi Najafi, E. Khaleghi, A new restarting method in the Arnoldi algorithm for computing the eigenvalues of a nonsymmetric matrix, Appl. Math. 156 (2004) 59–71] and develop a new algorithm for finding the eigenvalues of a nonsymmetric matrix on the basis of Arnoldi algorithm. In most of the restarting methods the basic idea is the selection of the best initial eigenvector, but our aim is to improve the initial eigenvectors in each iteration of the restarting method. Numerical tests show the algorithm converges rapidly with high accuracy.