连续Sylvester矩阵方程求解的分裂迭代算法

A Splitting Iterative Algorithm for Solving Continuous Sylvester Matrix Equations

有效求解连续的Sylvester矩阵方程对于科学和工程计算有着重要的应用价值,因此该文提出了一种可行的分裂迭代算法.该算法的核心思想是外迭代将连续Sylvester矩阵方程的系数矩阵分裂为对称矩阵和反对称矩阵,内迭代求解复对称矩阵方程.相较于传统的分裂算法,该文所提出的分裂迭代算法有效地避免了最优迭代参数的选取,并利用了复对称方程组高效求解的特点,进而提高了算法的易实现性、易操作性.此外,从理论层面进一步证明了该分裂迭代算法的收敛性.最后,通过数值算例表明分裂迭代算法具有良好的收敛性和鲁棒性,同时也证实了分裂迭代算法的收敛性很大程度依赖于内迭代格式的选取.

The solution of continuous Sylvester matrix equations has significant application val ue in scientific and engineering calculations,hence,a splitting iterative algorithm was pro-posed.The core idea of the algorithm is to split the coefficient matrix of the continuous Sylves ter matrix equation into a symmetric matrix and an antisymmetric matrix with an outer iterative scheme,and to solve the complex symmetric matrix equation with the inner iterative scheme.Compared with the traditional splitting algorithms,the proposed splitting algorithm effectively avoids the selection of optimal iterative parameters and takes advantages of the efficient solu tion of complex symmetric equations,which improves the easy implementation and easy opera-tion of the algorithm.In addition,the convergence of the splitting iterative algorithm was fur ther proved theoretically.Numerical examples show that,the splitting iterative algorithm has good convergence and robustness,and the convergence of the splitting iterative algorithm de pends on the selection of the inner iterative schemes.