一类矩阵方程的最小二乘反自反矩阵解

摘要

In this paper a new iterative method is presented to find the least-squares anti-reflexive matrix solu-tions of the matrix equations. First gives a reflexive matrix and the definition of anti-reflexive matrices. Then put forward the iterative method of solving matrix equation group and research the minimum norm matrix equations of the least-squares anti-reflexive matrix solutions. Finally a numerical example is given to illustrate the effi-iciency of this iterative method.%针对一类矩阵方程组提出了一种新的迭代法求其最小二乘反自反解。首先给出了自反矩阵及反自反矩阵的定义；然后提出了求解矩阵方程组的迭代法，并针对此算法研究了矩阵方程组范数最小的最小二乘反自反矩阵解；最后通过算例阐述了这种迭代方法的有效性。