Circulant preconditioners for Hermitian Toeplitz systems. (English) Zbl 0684.65035

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.
Reviewer: H.Hollatz


65F10 Iterative numerical methods for linear systems
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