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 th...

In this paper we propose a new approach for calculating some eigenpairs of large sparse nonHermitian matrices. This method, called Multiple Explicitly Restarted Arnoldi (MERAM), is particularly well suited for environments that combine different parallel programming paradigms. This technique is based on a multiple use of Explicitly Restarted Arnoldi method and improves its convergence. This tec...

The explicitly restarted Arnoldi method (ERAM) allows one to find a few eigenpairs of a large sparse matrix. The multiple explicitly restarted Arnoldi method (MERAM) is a technique based upon a multiple projection of ERAM and accelerates its c S i t c a t ©

The Explicitly Restarted Arnoldi Method (ERAM) allows to find a few eigenpairs of a large sparse matrix. The Multiple Explicitly Restarted Arnoldi Method (MERAM) is a technique based upon a multiple projection of ERAM and accelerates its convergence [3]. The MERAM allows to update the restarting vector of an ERAM by taking the interesting eigen-information obtained by the other ones into accoun...

It is well known that the Lanczos process suffers from loss of orthogonality in the case of finite-precision arithmetic. Several approaches have been proposed in order to address this issue, thus enabling the successful computation of approximate eigensolutions. However, these techniques have been studied mainly in the context of long Lanczos runs, but not for restarted Lanczos eigensolvers. Se...

The nonsymmetric Lanczos algorithm, which belongs to the class of Krylov subspace methods, is increasingly being used for model reduction of large scale systems of the form f(s) = c (sI−A)−1b, to exploit the sparse structure and reduce the computational burden. However, a good approximation is, usually, achieved only with relatively high order reduced models. Moreover, the computational cost of...