Augmented implicitly restarted Lanczos bidiagonalization methods

被引：205
作者：
Baglama, J [1 ]
Reichel, L
机构：
[1] Univ Rhode Isl, Dept Math, Kingston, RI 02881 USA
[2] Kent State Univ, Dept Math Sci, Kent, OH 44242 USA
来源：
SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2005年 / 27卷 / 01期
关键词：
singular value computation; partial singular value decomposition; iterative method; large-scale computation;
D O I：
10.1137/04060593X
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：19 / 42
页数：24
相关论文
共 33 条
[21]   Deflation techniques for an implicitly restarted Arnoldi iteration [J].
Lehoucq, RB ;
Sorensen, DC .
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1996, 17 (04) :789-821
[22]   Implicitly restarted Arnoldi methods and subspace iteration [J].
Lehoucq, RB .
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2001, 23 (02) :551-562
[23]  
*MATHWORKS INC, 2002, MATLAB VERS 6 5 R13
[24]   COMPUTING INTERIOR EIGENVALUES OF LARGE MATRICES [J].
MORGAN, RB .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1991, 154 :289-309
[25]   On restarting the Arnoldi method for large nonsymmetric eigenvalue problems [J].
Morgan, RB .
MATHEMATICS OF COMPUTATION, 1996, 65 (215) :1213-1230
[26]  
MORGAN RB, 2003, HARMONIC RESTARTED A
[27]   APPROXIMATE SOLUTIONS AND EIGENVALUE BOUNDS FROM KRYLOV SUBSPACES [J].
PAIGE, CC ;
PARLETT, BN ;
VANDERVORST, HA .
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 1995, 2 (02) :115-133
[28]   Low-rank matrix approximation using the Lanczos bidiagonalization process with applications [J].
Simon, HD ;
Zha, HY .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2000, 21 (06) :2257-2274
[29]  
Sorensen DC, 2002, ACT NUMERIC, V11, P519
[30]   IMPLICIT APPLICATION OF POLYNOMIAL FILTERS IN A K-STEP ARNOLDI METHOD [J].
SORENSEN, DC .
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1992, 13 (01) :357-385
1234