期刊论文

中文

数学理论与应用

1006-8074

2016

36

1

25-30

湖南省研究生创新项目（CX2015B374）；

本校为第一机构

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Pm，这个预处理子P。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（Pm＊A）·＊（Pm＊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 t...