A dynamic thick restarted semi-refined ABLE algorithm for computing a few selected eigentriplets of large nonsymmetric matrices

ABLE method can be used to compute eigentriplets of large scale nonsymmetric matrices. However, there is no guarantee for the Ritz vectors obtained by this method to converge even if the subspace is good enough. Furthermore, for the sake of storage limitation and amount of computations, restarting techniques are often needed. In order to deal with these problems, we propose a dynamic thick restarted semi-refined ABLE algorithm (SABLE) in which we use semi-refined Ritz vectors to approximate the desired eigenvectors. The relationship between the novel method and the classical one is given. Theoretical results show that the new method can circumvent the possible danger that exists in the standard one in some degree. Numerical experiments are made on real world problems, and comparisons are drown on the thick restarted ABLE algorithm (TABLE) and the dynamic thick restarted semi-refined ABLE algorithm (SABLE). They show that the latter is often more powerful and attractive than its standard counterpart.