Paper Info
Title
An Implicitly Restarted Refined Bidiagonalization Lanczos Method for Computing a Partial Singular Value Decomposition
Abstract
The bidiagonalization Lanczos method can be used for computing a few of the largest or smallest singular values and corresponding singular vectors of a large matrix, but the method may encounter some convergence problems. In this paper the convergence of the method is analyzed, showing why it may converge erratically and perhaps fail to converge. To correct this possible nonconvergence and improve the method, a refined bidiagonalization Lanczos method is proposed. The implicitly restarting technique due to Sorensen is applied to the method, and an implicitly restarted refined bidiagonalization Lanczos algorithm (IRRBL) is developed. A new selection of shifts is proposed for use within IRRBL, called refined shifts, and a reliable and efficient algorithm is developed for computing the refined shifts. Numerical experiments show that IRRBL can perform better than the implicitly restarted bidiagonalization Lanczos algorithm (IRBL) proposed by Larsen, in particular when the smallest singular triplets are desired.
Year
DOI
Venue
2003
10.1137/S0895479802404192
SIAM J. Matrix Analysis Applications
Keywords
Field
DocType
smallest singular value,bidiagonalization lanczos method,partial singular value decomposition,refined bidiagonalization lanczos method,large matrix,smallest singular triplet,bidiagonalization lanczos algorithm,efficient algorithm,convergence problem,corresponding singular vector,refined shift,singular value decomposition,convergence,singular value
Convergence (routing),Linear algebra,Singular value decomposition,Mathematical optimization,Singular value,Lanczos resampling,Matrix (mathematics),Mathematical analysis,Lanczos algorithm,Bidiagonalization,Mathematics
Journal
Volume
Issue
ISSN
25
1
0895-4798
Citations 
PageRank 
References 
14
1.07
5
Authors
2
Name
Order
Citations
PageRank
Zhongxiao Jia112118.57
Datian Niu2262.90