An implicitly restarted bidiagonal Lanczos Method forLarge-scale singular value problems

Technical Report · Sat Aug 01 04:00:00 EDT 1998

DOI:https://doi.org/10.2172/6451· OSTI ID:6451

Wang, Xiaohui ^[1]; Zha, Hongyuan

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1. LBNL Library

Low rank approximation of large and/or sparse rectangular matrices is a very import ant topic in many application problems and is closely related to the sin- gular value decomposition of the matrices. In this paper, we propose an implicit restart scheme for the bidiagonal Lanczos algorithm to compute a subset of the dominating singular triplets. We also illustrate the connection of the method with inverse eigenvalue problems. In the Lanczos process, we use the so-called one-sided reorthogonalization strategy to maintain the orthogonality level of the Lanczos vec- tors. The efficiency and the applicability of our algorithm are illustrated by some numerical examples from information retrieval applications.

• Research Organization: Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, CA (US)
• Sponsoring Organization: USDOE Office of Science
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 6451
• Report Number(s): LBNL--42472; ON: DE00006451
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
Algorithms
Eigenvalues
Matrices
Vectors