求解Sylvester方程的正交迭代算法

Orthogonal Iterative Algorithm for Sylvester Equations

对于任意初始矩阵,运用求解Sylvester矩阵方程的正交迭代算法可以在有限步内得到方程的最小二乘解,而且通过选择初始矩阵还可以得到方程的极小范数最小二乘解,这种算法还能用于解决最佳逼近问题,数值例子表明了所提出算法的有效性。

In this paper ,an orthogonal iterative algorithm for solving Sylvester matrix equations is proposed. Using the iterative algorithm,a/east-square solution of Sylvester matrix equations for any initial matrix can be obtained within finite iteration steps. Furthermore,the least-square solution with the minimum norm can be obtained by choosing a special initial matrix. The algorithm can also be applied to solve optimal approximation problems, Finally, the algorithms is tested on computer and the results verify the theoretical findings.