THE NEAREST BISYMMETRIC SOLUTIONS OF LINEAR MATRIX EQUATIONS

• 来源期刊: 计算数学(英文版)
• 关键词: Bisymmetric matrix Matrix equation Matrix nearness problem Kroneckerproduct Frobenius norm Moore-Penrose generalized inverse.
• 年，卷（期）: 2004,（6）
• 页码范围: 873-880
• 页数: 8页
• 语种: 英文

摘要

The necessary and sufficient conditions for the existence of and the expressions for bismmetric soutions of the matrix equation(Ⅰ)A1X1B1+A2X2B2+…AkXkBk=D,(Ⅱ)A1XB1+A2XB2+…+AkXBk=D and (Ⅲ)(A1XB1,A2XB2,…,AkXBK)=(D1,D2,…,Dk) are derived by using kronecker product and Moore-Penrose generalized inverse of matrices. In addition, in corresponding solution set of the matrix equations, the explicit expression of the nearest matrix to a given matrix in the Frobenius norm is given.Numerical methods and numerical experiments of finding the nearest solutions are also provided.