广义耦合Sylvester矩阵方程的对称-反对称最小二乘解  

The Least Squares Symmetric-skew Symmetric Solution of the Generalized Coupled Sylvester Matrix Equations

作　　者：梁开福[1] 刘建州[1] 

机构地区：[1]湘潭大学数学与计算科学学院,湖南湘潭411105

出　　处：《应用数学》2011年第4期746-753,共8页Mathematica Applicata

基　　金：国家自然科学基金资助项目(10971176);湖南省自然科学基金资助项目(10JJ2002)

摘　　要：本文主要研究极小残差问题=min关于X对称-Y反对称解的迭代算法.本文首先给出等价于极小残差问题的规范方程,然后,提出求解此规范方程的对称-反对称解的迭代算法.在不考虑舍入误差的情况下,任取一个初始的对称-反对称矩阵对(X0,Y0),该算法都可以在有限步内求得该极小残差问题的对称-反对称解.最后讨论该问题的极小范数对称-反对称解.In this paper,an iterative method is proposed for solving the minimum residual =min over X symmetric-Y skew symmetric.First,it is obtained that the normal equations equivalent to the minimum residual problem,and then an iterative algorithm is presented for solving the normal matrix equations.By using the iterative method,the least squares symmetric-skew symmetric solution can be got within finite iteration steps in the absence of roundoff errors for any initial symmetric-skew symmetric matrix pair （X0,Y0）.Moreover,the least squares symmetric-skew symmetric solution with minimum norm can be got by choosing a special kind of initial matrix.

关 键 词：矩阵方程 极小残差问题 迭代算法 最小二乘解 对称-反对称解 

分 类 号：O241.6[理学—计算数学]