Hartley preconditioners for Toeplitz systems generated by positive continuous functions (Q1338529)

The solution of a positive definite Toeplitz system of linear equations by the preconditioned conjugate gradient method is discussed. It is shown that if the generating function of the coefficient matrix is a positive \(2 \pi\)-periodic continuous even function, then the preconditioned conjugate gradient method has superlinear convergence. The paper extends the result of \textit{D. Bini} and \textit{P. Favati} [SIAM J. Matrix Anal. Appl. 14, No. 2, 500-507 (1993; Zbl 0773.65029)] for the Wiener class of \(2 \pi\)-periodic continuous functions.