Generalization of the Sherman-Morrison-Woodbury formula involving the Schur complement
文献类型：期刊论文
| 作者 | Xu, Xuefeng |
| 刊名 | APPLIED MATHEMATICS AND COMPUTATION
 |
| 出版日期 | 2017-09-15 |
| 卷号 | 309页码:183-191 |
| 关键词 | Sherman-Morrison-Woodbury formula Moore-Penrose inverse Schur complement |
| ISSN号 | 0096-3003 |
| DOI | 10.1016/j.amc.2017.03.039 |
| 英文摘要 | Let X is an element of C-mxm and Y is an element of C-nxn be nonsingular matrices, and let N is an element of C-mxn. Explicit expressions for the Moore-Penrose inverses of M = XNY and a two-by-two block matrix, under appropriate conditions, have been established by Castro-Gonzalez et al. [Linear Algebra Appl. 471 (2015) 353-368]. Based on these results, we derive a novel expression for the Moore-Penrose inverse of A+UV* under suitable conditions, where A is an element of C-mxn, U is an element of C-mxr, and V is an element of C-nxr In particular, if both A and I + V*A(-1)U are nonsingular matrices, our expression reduces to the celebrated Sherman-Morrison-Woodbury formula. Moreover, we extend our results to the bounded linear operators case. (C) 2017 Elsevier Inc. All rights reserved. |
| 语种 | 英语 |
| WOS记录号 | WOS:000401598800014 |
| 出版者 | ELSEVIER SCIENCE INC |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/25390]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Xu, Xuefeng |
| 作者单位 | Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Xu, Xuefeng. Generalization of the Sherman-Morrison-Woodbury formula involving the Schur complement[J]. APPLIED MATHEMATICS AND COMPUTATION,2017,309:183-191. |
| APA | Xu, Xuefeng.(2017).Generalization of the Sherman-Morrison-Woodbury formula involving the Schur complement.APPLIED MATHEMATICS AND COMPUTATION,309,183-191. |
| MLA | Xu, Xuefeng."Generalization of the Sherman-Morrison-Woodbury formula involving the Schur complement".APPLIED MATHEMATICS AND COMPUTATION 309(2017):183-191. |
入库方式： OAI收割
来源：数学与系统科学研究院
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