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LOW-RANK MATRIX APPROXIMATION USING THE LANCZOS BIDIAGONALIZATION PROCESS WITH APPLICATIONS.
- Source :
-
SIAM Journal on Scientific Computing . 2000, Vol. 21 Issue 6, p2257-2274. 18p. - Publication Year :
- 2000
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *SPARSE matrices
*ALGORITHMS
*NUMERICAL analysis
*MATHEMATICS
*ALGEBRA
Subjects
Details
- Language :
- English
- ISSN :
- 10648275
- Volume :
- 21
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Scientific Computing
- Publication Type :
- Academic Journal
- Accession number :
- 13204880
- Full Text :
- https://doi.org/10.1137/S1064827597327309