Deflation Techniques for an Implicitly Restarted Arnoldi Iteration
Sorensen, Danny C.
A deflation procedure is introduced that is designed to improve 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 deflation 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 purgingoperation, 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.
Citable link to this pagehttps://hdl.handle.net/1911/101832
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