The matrix nearness problem for symmetric matrices associated with the matrix equation [ATXA, BTXB] = [C, D]

被引：13

作者：

Liao, An-ping ^{[1
]}

Lei, Yuan

Yuan, Shi-fang

机构：

[1] Hunan Univ, Coll Math & Econometr, Changsha 410082, Peoples R China

[2] Changsha Univ, Dept Comp & Informat Sci, Changsha 410003, Peoples R China

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2006年 / 418卷 / 2-3期

关键词：

symmetric matrix; least-squares solution; optimal approximate solution; generalized singular value decomposition; canonical correlation decomposition;

D O I：

10.1016/j.laa.2006.03.032

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A direct method, based on the projection theorem in inner products spaces, the generalized singular value decomposition and the canonical correlation decomposition, is presented for finding the optimal approximate solution (X) over cap in the set S-E to a given matrix, where SE denotes the least-squares symmetric solution set of the matrix equation [A(T)XA, (BXB)-X-T] = [C, D]. The analytical expression of the optimal approximate solution (X) over cap is obtained, and an algorithm for finding this solution is also suggested. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：939 / 954

页数：16

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