大型连续Sylvester方程外推的CSCS迭代  

Extrapolated CSCS Iterations of Large Continuous Sylvester Equations

作　　者：刘仲云 张芳 Liu Zhongyun;Zhang Fang(School of Mathematics and Statistics,Changsha University of Science and Technology,Changsha 410114,China)

机构地区：[1]长沙理工大学数学与统计学院,长沙410114

出　　处：《数学理论与应用》2022年第2期120-126,共7页Mathematical Theory and Applications

基　　金：国家自然科学基金项目(No.11371075)资助。

摘　　要：文献[1]提出了当系数矩阵A,B都是正定Toeplitz矩阵时求解连续Sylvester方程AX+XB=E的循环反循环分裂迭代(CSCS迭代)方法.为了提高这个方法的收敛速度,本文提出外推的CSCS迭代,讨论其收敛性,并通过数值实验验证其有效性.In reference[1],a circulant and skew-circulant splitting iterative method(CSCS iteration)for solving the continuous Sylvester equation AX+XB=E is proposed,where the coefficients A and B are both positive definite Toeplitz matrices.In order to improve the convergence speed of this method,we propose an extrapolated CSCS iteration,discuss its convergence and show its effectiveness by numerical experiments.

关 键 词：SYLVESTER方程 TOEPLITZ矩阵 循环矩阵 反循环矩阵 收敛性 

分 类 号：O241.6[理学—计算数学]