Fast iterative solvers for symmetric Toeplitz systems - A survey and an extension

被引:32
作者
Jin, XQ [1 ]
机构
[1] UNIV MACAU, FAC SCI & TECHNOL, Taipa, Macao, PEOPLES R CHINA
关键词
Toeplitz matrix; circulant preconditioner; sine-transform preconditioner; Hartley-transform preconditioner; PCG method;
D O I
10.1016/0377-0427(95)00156-5
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Fast iterative Toeplitz solvers based on the preconditioned conjugate gradient (PCG) methods with circulant preconditioners were proposed in 1985. Since then, Sine-transform preconditioner and Hartley-transform preconditioner were proposed in 1990 and 1993, respectively. For solving a large family of Toeplitz systems T(n)x = b, it requires only O(n log n) operations by using these preconditioners. In this paper, we give a brief survey and unify the analysis of all these preconditioners. An extension to the block Toeplitz systems is also given here.
引用
收藏
页码:315 / 321
页数:7
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