Fast iterative solvers for symmetric Toeplitz systems — A survey and an extension
Proceedings of the 6th international congress on Computational and applied mathematics(1996)
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 Tnx = 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.
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关键词
Toeplitz matrix,Circulant preconditioner,Sine-transform preconditioner,Hartley-transform preconditioner,PCG method
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