Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 21, Issue 6, Pages 2257-2274Publisher
SIAM PUBLICATIONS
DOI: 10.1137/S1064827597327309
Keywords
singular value decomposition; space matrices; Lanczos algorithms; low-rank approximation
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Low-rank approximation of large and/or sparse matrices is important in many applications, and the singular value decomposition (SVD) gives the best low-rank approximations with respect to unitarily-invariant norms. In this paper we show that good low-rank approximations can be directly obtained from the Lanczos bidiagonalization process applied to the given matrix without computing any SVD. We also demonstrate that a so-called one-sided reorthogonalization process can be used to maintain an adequate level of orthogonality among the Lanczos vectors and produce accurate low-rank approximations. This technique reduces the computational cost of the Lanczos bidiagonalization process. We illustrate the efficiency and applicability of our algorithm using numerical examples from several applications areas.
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