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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:
65F20Overdetermined systems, pseudoinverses (numerical linear algebra)
65F10Iterative methods for linear systems
65F50Sparse matrices (numerical linear algebra)
Software:
PROPACK; ARPACK