Least Squares Symmetrizable Solutions for a Class of Matrix Equations

• 作者: Fanliang Li
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: MATRIX Equations MATRIX ROW STACKING TOPOLOGICAL ISOMORPHISM Least SQUARES Solution Optimal Approximation
• 年，卷（期）: yysxyw_2013,（5）
• 页码范围: 741-745
• 页数: 5页
• 分类号: O1

摘要

In this paper, we discuss least squares symmetrizable solutions of matrix equations (AX = B, XC = D) and its optimal approximation solution. With the matrix row stacking, Kronecker product and special relations between two linear subspaces are topological isomorphism, and we derive the general solutions of least squares problem. With the invariance of the Frobenius norm under orthogonal transformations, we obtain the unique solution of optimal approximation problem. In addition, we present an algorithm and numerical experiment to obtain the optimal approximation solution.