Some new restart vectors for explicitly restarted Arnoldi method

Abstract

The explicitly restarted Arnoldi method (ERAM) can be used to find some eigenvalues of large and sparse matrices. However, it has been shown that even this method may fail to converge. In this paper, we present two new methods to accelerate the convergence of ERAM algorithm. In these methods, we apply two strategies for the updated initial vector in each restart cycles. The implementation of the methods have been tested by numerical examples. The results show that we can obtain a good acceleration of the convergence compared to original ERAM.