Some new restart vectors for explicitly restarted Arnoldi method

The explicitly restarted Arnoldi method (ERAM) can be used to nd some eigenvalues of large and sparse matri- ces. 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 algo- rithm. 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 nu- merical examples. The results show that we can obtain a good acceleration of the convergence compared to orig- inal ERAM.