Best approximate solution of matrix equation AXB+CY D=E

doi:10.1137/040615791

	Best approximate solution of matrix equation AXB+CY D=E
	Liao, AP ; Bai, ZZ; Lei, Y
	2005
发表期刊	SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
ISSN	0895-4798
卷号	27 期号:3 页码:675-688
摘要	We derive an analytical expression of the best approximate solution in the least-squares solution set SE of the matrix equation AXB + CYD = E to a given matrix pair (X-f, Y-f), where A, B, C, D, and E are given matrices of suitable sizes. Our work is based on the projection theorem in the finite-dimensional inner product space, and we use the generalized singular value decomposition and the canonical correlation decomposition. Moreover, we establish a direct method for computing this best approximate solution. An algorithm for finding the best approximate solution is described in detail, and an example is used to show the feasibility and effectiveness of our algorithm.
关键词	matrix equation least-squares solution best approximate solution generalized singular value decomposition canonical correlation decomposition
DOI	10.1137/040615791
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000236098800006
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/1331
专题	计算数学与科学工程计算研究所
通讯作者	Liao, AP
作者单位	1.Hunan Univ, Coll Math & Economet, Changsha 410082, Peoples R China 2.Fudan Univ, Dept Math, Shanghai 200433, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Comp Math & Sci Engn Comp, State Key Lab Sci Engn Comp, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Liao, AP,Bai, ZZ,Lei, Y. Best approximate solution of matrix equation AXB+CY D=E[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,2005,27(3):675-688.
APA	Liao, AP,Bai, ZZ,&Lei, Y.(2005).Best approximate solution of matrix equation AXB+CY D=E.SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,27(3),675-688.
MLA	Liao, AP,et al."Best approximate solution of matrix equation AXB+CY D=E".SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 27.3(2005):675-688.