Least squares solution of BXAT = T over symmetric, skew-symmetric, and positive semidefinite X

被引：23

作者：

Deng, YB ^{[1
]}

Hu, XY ^{[1
]}

Zhang, L ^{[1
]}

机构：

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

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2003年 / 25卷 / 02期

关键词：

matrix equation; least squares problem; QSVD factorization; Hadamard product;

D O I：

10.1137/S0895479802402491

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An efficient method based on the quotient singular value decomposition (QSVD) is used to solve the constrained least squares problem min parallel toT-BXA(T)parallel to(F) over symmetric, skew-symmetric, and positive semidefinite (maybe asymmetrical) X. The general expression of the solution is given and some necessary and sufficient conditions are derived about the solvability of the matrix equation BXA(T) = T. In each case, an algorithm is given for the unique solution when B and A are of full column rank.

引用

页码：486 / 494

页数：9

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