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Augmented implicitly restarted Lanczos bidiagonalization methods. (English) Zbl 1087.65039

Summary: 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.

MSC:

65F20 Numerical solutions to overdetermined systems, pseudoinverses
65F10 Iterative numerical methods for linear systems
65F50 Computational methods for sparse matrices
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