KMS Of Academy of mathematics and systems sciences, CAS
| AN EFFICIENT GAUSS-NEWTON ALGORITHM FOR SYMMETRIC LOW-RANK PRODUCT MATRIX APPROXIMATIONS | |
Liu, Xin1 ; Wen, Zaiwen2; Zhang, Yin3
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| 2015 | |
| Source Publication | SIAM JOURNAL ON OPTIMIZATION
 |
| ISSN | 1052-6234 |
| Volume | 25Issue:3Pages:1571-1608 |
| Abstract | We derive and study a Gauss-Newton method for computing a symmetric low-rank product XXT, where X is an element of R-nxk for k < n, that is the closest to a given symmetric matrix A is an element of R-nxn in Frobenius norm. When A = (BB)-B-T (or BBT), this problem essentially reduces to finding a truncated singular value decomposition of B. Our Gauss-Newton method, which has a particularly simple form, shares the same order of iteration-complexity as a gradient method when k << n, but can be significantly faster on a wide range of problems. In this paper, we prove global convergence and a Q-linear convergence rate for this algorithm and perform numerical experiments on various test problems, including those from recently active areas of matrix completion and robust principal component analysis. Numerical results show that the proposed algorithm is capable of providing considerable speed advantages over Krylov subspace methods on suitable application problems where high-accuracy solutions are not required. Moreover, the algorithm possesses a higher degree of concurrency than Krylov subspace methods, thus offering better scalability on modern multi-/many-core computers. |
| Keyword | eigenvalue decomposition singular value decomposition low-rank product matrix approximation Gauss-Newton methods |
| DOI | 10.1137/140971464 |
| Language | 英语 |
| Funding Project | NSFC[11101409] ; NSFC[11331012] ; NSFC[91330115] ; NSFC[11322109] ; NSFC[91330202] ; NSFC[DMS-1115950] ; National Center for Mathematics and Interdisciplinary Sciences, CAS ; National Basic Research Project[2015CB856000] ; ONR grant[N00014-08-1-1101] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000362418100015 |
| Publisher | SIAM PUBLICATIONS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/20926 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Liu, Xin |
| Affiliation | 1.Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Sci & Engn Comp, Beijing 100864, Peoples R China 2.Peking Univ, Beijing Int Ctr Math Res, Beijing 100871, Peoples R China 3.Rice Univ, Dept Computat & Appl Math, Houston, TX 77005 USA |
| Recommended Citation GB/T 7714 | Liu, Xin,Wen, Zaiwen,Zhang, Yin. AN EFFICIENT GAUSS-NEWTON ALGORITHM FOR SYMMETRIC LOW-RANK PRODUCT MATRIX APPROXIMATIONS[J]. SIAM JOURNAL ON OPTIMIZATION,2015,25(3):1571-1608. |
| APA | Liu, Xin,Wen, Zaiwen,&Zhang, Yin.(2015).AN EFFICIENT GAUSS-NEWTON ALGORITHM FOR SYMMETRIC LOW-RANK PRODUCT MATRIX APPROXIMATIONS.SIAM JOURNAL ON OPTIMIZATION,25(3),1571-1608. |
| MLA | Liu, Xin,et al."AN EFFICIENT GAUSS-NEWTON ALGORITHM FOR SYMMETRIC LOW-RANK PRODUCT MATRIX APPROXIMATIONS".SIAM JOURNAL ON OPTIMIZATION 25.3(2015):1571-1608. |
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