非埃米特正定Toeplitz矩阵的m—步预处理子（英文）  

m—step Preconditioners for Nonhermitian Positive Definite Toeplitz Systems

作　　者：刘仲云[1] 于静[1] 张艳[1] 张育林 

机构地区：[1]长沙理工大学数学与统计学院,长沙410004 [2]Minho大学数学中心

出　　处：《数学理论与应用》2016年第1期25-30,共6页Mathematical Theory and Applications

基　　金：湖南省研究生创新项目(CX2015B374)

摘　　要：众所周知,如果A是Toeplitz矩阵,那么矩阵A有一循环与反循环分裂(记为CSCS)[7],可写为A=C+S,其中C为循环矩阵,S为反循环矩阵.本文针对某类Toeplitz矩阵,提出了一个m步的预处理子P_m,这个预处理子P_m是基于CSCS迭代方法构建的.本文中证明当C和S都是正定矩阵时,对于适当的m,预处理矩阵(P_m*A)**(P_m*A)的谱半径聚集于1.实验结果表明,对于适当的m,本文提出的预处理子优于T—Chan预处理子[3].It is known that ifA is a Toeplitz matrix, thenA enjoys a circulant and skew circulant splitting （de- noted by CSCS）, i. e. , A = C-b S with C a circulant matrix and S a skew circulant matrix. Based on the CSCS iteration [-7], we give m -- step preconditioners Pm for certain classes of Toeplitz matrices in this paper. We show that if both C and S are positive definite, then the spectrum of the preconditioned matrix （PmA） ＊ PnA are clustered around one for some moderate size m. Experimental results show that the proposed preconditioners perform slightly better than T. Chan＇s preconditioners in I-3] for some moderate size rn

关 键 词：循环与反循环分裂m-步多项式预处理子 共轭梯度方法Toeplitz矩阵 

分 类 号：O241.6[理学—计算数学]