THE JOINT BIDIAGONALIZATION OF A MATRIX PAIR WITH INACCURATE INNER ITERATIONS
文献类型：期刊论文
| 作者 | Li, Haibo1,2 |
| 刊名 | SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
 |
| 出版日期 | 2024 |
| 卷号 | 45期号:1页码:232-259 |
| 关键词 | joint bidiagonalization GSVD inner iteration stopping tolerance Lanczos bidiag- onalization convergence and accuracy |
| ISSN号 | 0895-4798 |
| DOI | 10.1137/22M1541083 |
| 英文摘要 | The joint bidiagonalization (JBD) process iteratively reduces a matrix pair {A, L\} to two bidiagonal forms simultaneously, which can be used for computing a partial generalized singular value decomposition (GSVD) of {A, L\} . The process has a nested inner-outer iteration structure, where the inner iteration usually cannot be computed exactly. In this paper, we study the inaccurately computed inner iterations of JBD by first investigating the influence of computational error of the inner iteration on the outer iteration, and then proposing a reorthogonalized JBD (rJBD) process to keep orthogonality of a part of Lanczos vectors. An error analysis of the rJBD is carried out to build up connections with Lanczos bidiagonalizations. The results are then used to investigate convergence and accuracy of the rJBD based GSVD computation. It is shown that the accuracy of computed GSVD components depends on the computing accuracy of inner iterations and the condition number of (AT, LT )T , while the convergence rate is not affected very much. For practical JBD based GSVD computations, our results can provide a guideline for choosing a proper computing accuracy of inner iterations in order to obtain approximate GSVD components with a desired accuracy. Numerical experiments are made to confirm our theoretical results. |
| 资助项目 | National Natural Science Foundation of China[3192270206] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:001171693500005 |
| 出版者 | SIAM PUBLICATIONS |
| 源URL | [http://119.78.100.204/handle/2XEOYT63/38704]  |
| 专题 | 中国科学院计算技术研究所期刊论文_英文 |
| 通讯作者 | Li, Haibo |
| 作者单位 | 1.Chinese Acad Sci, Inst Comp Technol, Beijing 100190, Peoples R China 2.Huawei Technol, Comp Syst Optimizat Lab, Beijing 100094, Peoples R China |
| 推荐引用方式 GB/T 7714 | Li, Haibo. THE JOINT BIDIAGONALIZATION OF A MATRIX PAIR WITH INACCURATE INNER ITERATIONS[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,2024,45(1):232-259. |
| APA | Li, Haibo.(2024).THE JOINT BIDIAGONALIZATION OF A MATRIX PAIR WITH INACCURATE INNER ITERATIONS.SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,45(1),232-259. |
| MLA | Li, Haibo."THE JOINT BIDIAGONALIZATION OF A MATRIX PAIR WITH INACCURATE INNER ITERATIONS".SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 45.1(2024):232-259. |
入库方式： OAI收割
来源：计算技术研究所
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