A new method for accelerating Arnoldi algorithms for large scale eigenproblems

Abstract

We propose a new method for accelerating the convergence of the implicitly restarted Arnoldi (IRA) algorithm for the solution of large sparse nonsymmetric eigenvalue problems. A new relationship between the residual of the current step and the residual in the previous step is derived and we use this relationship to develop a technique for dynamically switching the Krylov subspace dimension at successive cycles. We give numerical results for various difficult nonsymmetric eigenvalue problems that demonstrate the capability of the dynamic switching strategy for significantly accelerating the convergence of Arnoldi algorithms. For some large scale difficult eigenvalue problems that arise in the fields of computational fluid dynamics, electrical engineering and materials science, our strategy leads to significant reductions in the number of matrix–vector products, orthogonalization costs and computational time.