D反对称矩阵反问题的最小二乘解

来源期刊：中南大学学报(自然科学版)2001年第5期

论文作者：张忠志 周富照 胡锡炎

文章页码：545 - 548

关键词：D反对称矩阵;矩阵范数;最佳逼近

Key words：D-untisymmetric matrices; matrix norm; optimal approximation

摘    要：为了研究约束矩阵方程问题,提出了D反对称矩阵的概念,研究了D反对称矩阵反问题的最小二乘解及其最佳逼近问题;采用矩阵奇异值分解、分块降阶等方法,获得了D反对称矩阵反问题的最小二乘解一般表达式及最佳逼近解的表达式,并对其逆特值问题、线性约束方程问题给出了有解的充分必要条件,推广了文献[1]中的相关结果及应用范围.

Abstract: A conceptof D-antisysmmetric matrices was putout. The least-square solutions of inverse problems for D-an-tisymmetric matrices and theiroptimal approximation are considered. Ageneral representation of the solutions of the least- square problem and the expression of the optimal approximation solution by exploiting amatrixfactorization or a dimension decreasingmethod was given. Necessary and sufficient conditions for the solvability of inverse eigenvalue proble mand linear constraints matrix equation problem are proposed. The theorem of the conference[1] was extended.