Abstract
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.
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