Generalization of the Sherman-Morrison-Woodbury formula involving the Schur complement

doi:10.1016/j.amc.2017.03.039

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	Generalization of the Sherman-Morrison-Woodbury formula involving the Schur complement
	Xu, Xuefeng
	2017-09-15
发表期刊	APPLIED MATHEMATICS AND COMPUTATION
ISSN	0096-3003
卷号	309 页码:183-191
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.
关键词	Sherman-Morrison-Woodbury formula Moore-Penrose inverse Schur complement
DOI	10.1016/j.amc.2017.03.039
语种	英语
资助项目	Science Challenge Project[JCKY201612A503-1-303] ; National Natural Science Foundation of China[91430215] ; National Natural Science Foundation of China[91530323]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000401598800014
出版者	ELSEVIER SCIENCE INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/25391
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.