Extended Lanczos bidiagonalization algorithm for low rank approximation and its applications

被引：1

作者：

Wang, Xuansheng ^{[1
]}

Glineur, Francois ^{[2
]}

Lu, Linzhang ^{[3
]}

Van Dooren, Paul ^{[4
,5
]}

机构：

[1] Shenzhen Inst Informat Technol, Software Engn, Shenzhen, Peoples R China

[2] Catholic Univ Louvain, CORE, B-1348 Louvain La Neuve, Belgium

[3] Guizhou Normal Univ, Sch Math & Comp Sci, Guizhou, Peoples R China

[4] Catholic Univ Louvain, ICTEAM Inst, B-1348 Louvain La Neuve, Belgium

[5] Xiamen Univ, Sch Math Sci, Xiamen, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2016年 / 301卷

基金：

中国国家自然科学基金;

关键词：

Low rank approximation; Singular value decomposition; Lanczos bidiagonalization; RECOGNITION;

D O I：

10.1016/j.cam.2015.12.039

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose an extended Lanczos bidiagonalization algorithm for finding a low rank approximation of a given matrix. We show that this method can yield better low-rank approximations than standard Lanczos bidiagonalization algorithm, without increasing the cost too much. We also describe a partial reorthogonalization process that can be used to maintain an adequate level of orthogonality of the Lanczos vectors in order to produce accurate low-rank approximations. We demonstrate the effectiveness and applicability of our algorithm for a number of applications. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：213 / 229

页数：17

共 50 条

[1] Low-rank matrix approximation using the Lanczos bidiagonalization process with applications
Simon, HD
Zha, HY
[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2000, 21 (06): : 2257 - 2274
[2] A Lanczos bidiagonalization algorithm for Hankel matrices
Browne, Kevin
Qiao, Sanzheng
Wei, Yimin
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 430 (5-6) : 1531 - 1543
[3] PROBABILISTIC BOUNDS FOR THE MATRIX CONDITION NUMBER WITH EXTENDED LANCZOS BIDIAGONALIZATION
Gaaf, Sarah W.
Hochstenbach, Michiel E.
[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2015, 37 (05): : S581 - S601
[4] Structured low-rank approximation and its applications
Markovsky, Ivan
[J]. AUTOMATICA, 2008, 44 (04) : 891 - 909
[5] LOW-RANK MODIFICATION OF THE UNSYMMETRIC LANCZOS-ALGORITHM
HUCKLE, T
[J]. MATHEMATICS OF COMPUTATION, 1995, 64 (212) : 1577 - 1588
[6] A BLOCK BIDIAGONALIZATION METHOD FOR FIXED-ACCURACY LOW-RANK MATRIX APPROXIMATION
Hallman, Eric
[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2022, 43 (02) : 661 - 680
[7] An algorithm for low-rank matrix factorization and its applications
Chen, Baiyu
Yang, Zi
Yang, Zhouwang
[J]. NEUROCOMPUTING, 2018, 275 : 1012 - 1020
[8] On accuracy properties of one-sided bidiagonalization algorithm and its applications
Bosner, N
Drmac, Z
[J]. Proceedings of the Conference on Applied Mathematics and Scientific Computing, 2005, : 141 - 150
[9] A Fast Algorithm for a Weighted Low Rank Approximation
Dutta, Aritra
Li, Xin
[J]. PROCEEDINGS OF THE FIFTEENTH IAPR INTERNATIONAL CONFERENCE ON MACHINE VISION APPLICATIONS - MVA2017, 2017, : 93 - 96
[10] On Approximation Algorithm for Orthogonal Low-Rank Tensor Approximation
Yang, Yuning
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2022, 194 (03) : 821 - 851

← 1 2 3 4 5 →