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Zbl 0684.65035
Chan, Raymond H.
Circulant preconditioners for Hermitian Toeplitz systems. (English)
[J] SIAM J. Matrix Anal. Appl. 10, No.4, 542-550 (1989). ISSN 0895-4798; ISSN 1095-7162/e

The preconditioned conjugate gradient method for three families of circulant preconditioners for solving a linear system with a Hermitian positive definite Toeplitz matrix is studied. Superlinear convergence rates of all iterative methods are proved. For a Toeplitz matrix with entries that are Fourier coefficients of a positive function f in the Wiener class a very good error estimation for the conjugate gradient steps is proved. A numerical example illustrates the convergence behavior.
[H.Hollatz]

MSC 2000:: *65F10 Iterative methods for linear systems

Keywords: preconditioned conjugate gradient method; circulant preconditioners; Hermitian positive definite Toeplitz matrix; Superlinear convergence rates; Fourier coefficients; positive function; Wiener class; error estimation; numerical example

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