Deflation Techniques for an Implicitly Re-started Arnoldi Iteration.

摘要

A deflation procedure is introduced that is designed to improve the convergence of an implicitly restarted Arnoldi iteration for computing a few eigenvalues of a large matrix. As the iteration progresses the Ritz value approximations of the eigenvalues of A converge at different rates, A numerically stable scheme is introduced that implicitly deflates the converged approximations from the iteration. We present two forms of implicit deflation. The first, a locking operation, decouples converged Ritz values and associated vectors from the active part of the iteration. The second, a purging operation, removes unwanted but converged Ritz pairs. Convergence of the iteration is improved and a reduction in computational effort is also achieved. The deflation strategies make it possible to compute multiple or clustered eigenvalues with a single vector restart method. A Block method is not required. These schemes are analyzed with respect to numerical stability and computational results are presented.