2005•SIAM Journal on Scientific ComputingOpen access

Augmented Implicitly Restarted Lanczos Bidiagonalization Methods

James Baglama, Lothar Reichel

Abstract

New restarted Lanczos bidiagonalization methods for the computation of a few of the largest or smallest singular values of a large matrix are presented. Restarting is carried out by augmentation of Krylov subspaces that arise naturally in the standard Lanczos bidiagonalization method. The augmenting vectors are associated with certain Ritz or harmonic Ritz vectors. Computed examples show the new methods to be competitive with available schemes.

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Key concepts: Lanczos resampling, Mathematics, Lanczos algorithm, Applied mathematics, Linear subspace, Krylov subspace, Computation, Ritz method