基于梯度的Sylvester共轭矩阵方程的迭代解

Gradient Based Iterative Solutions for Sylvester-Conjugate Matrix Equations

中文关键词:  Sylvester共轭矩阵方程  迭代法  收敛  松弛参数

英文关键词:Sylvester-conjugate matrix equations  iterative solutions  convergence  relaxation parameter

中文摘要:

      本文提出了一种基于梯度的Sylvester共轭矩阵方程的迭代算法.通过引入一个松弛参数和采用递阶辨识原理,构造一个迭代算法求解Sylvester矩阵方程.通过应用复矩阵的实数表达以及实数表示的一些性质,收敛性分析表明在一定假设条件下,对于任意初始值,迭代方法均收敛到精确解,数值算例也表明了所给方法的有效性.

英文摘要:

      This paper presents a gradient based iterative algorithm for Sylvester-conjugate matrix equations with a unique solution. By introducing a relaxation parameter and applying the hierarchical identification principle, an iterative algorithm is constructed to solve Sylvester matrix equations. By applying a real representation of a complex matrix as a tool and using some properties of the real representation, convergence analysis indicates that the iterative solutions converge to the exact solutions for any initial values under certain assumptions. Numerical examples are given to illustrate the efficiency of the proposed approach.