子阵约束下矩阵方程AX=B反问题的实反对称解及其最佳逼近  

Real Anti-Symmetric Solutions of Inverse Problem of the Matrix Equation AX=B under a Submatrix Constraint and Its Optimal Approximation

作　　者：陈亚波[1] 

机构地区：[1]湖南农业大学理学院,湖南长沙410128

出　　处：《湖南农业大学学报（自然科学版）》2002年第5期444-446,共3页Journal of Hunan Agricultural University(Natural Sciences)

摘　　要：利用矩阵的奇异值分解及广义逆 ,给出了子矩阵约束下矩阵方程 AX=B反问题有实反对称解的充分必要条件及其通解的表达式 .另外 。Inverse probles of matricem have been widely used in fields of structure design and automatic control .By using the singular value decomposition (SVD)and Moore-Penrose inverse of matrices, this paper establishes the necessary and sufficient conditions for the existence of and the expressions for the anti-symmetric solutions of inverse problem of the matrix equation AX = B under a submatrix constraint. In addition, in the solution set of corresponding problem, the expression of the optimal approximation solution to a given matrix is derived,and a numerical algorithm and a numerical example for solving optimal approximation solution are included.

关 键 词：子阵约束 矩阵方程 实反对称解 反对称矩阵 反问题 最佳逼近 广义逆 数值算法 

分 类 号：O241.6[理学—计算数学]