广义Sylvester矩阵方程AX+YA=C一般解的正交投影迭代解法

An Orthogonal Projection Iteration Method for the General Real Solution of Generalized Sylvester Matrix Equations AX+YA=C

本文讨论了广义Sylvester矩阵方程AX+YA=C的一般实数解及其最佳逼近的正交投影迭代解法,首先利用正交投影及奇异值分解,构造迭代算法,证明了算法的收敛性,得出了收敛速率的估计式;其次给出数值实例,验证了算法的有效性。

The general real solution of generalized Sylvester matrix equations AX+YA=C and the orthog-onal projection iteration method to optimal approximation are studied. Firstly, the iterative method is constructed and its convergence is proved by using the theory of orthogonal projection and the singular value decomposition, and the estimation of its convergence rate is obtained;secondly, nu-merical examples are given to verify the validity of the algorithm.