Chan, Raymond H. Circulant preconditioners for Hermitian Toeplitz systems. (English) Zbl 0684.65035 SIAM J. Matrix Anal. Appl. 10, No. 4, 542-550 (1989). 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 Cited in 50 Documents MSC: 65F10 Iterative numerical 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 PDFBibTeX XMLCite \textit{R. H. Chan}, SIAM J. Matrix Anal. Appl. 10, No. 4, 542--550 (1989; Zbl 0684.65035) Full Text: DOI Link