A family of modified regularizing circulant preconditioners for two-levels Toeplitz systems

Customary circulant preconditioners of Chan, Strang, and inverse-Toeplitz type are modified for the regularized solution of ill-conditioned Toeplitz systems. Given a symmetric two-level Toeplitz matrix A, and two parameters tau and sigma, consider the customary preconditioner C and modify it by replacing its eigenvalues with-modulus less than tau with the value alpha. The circulant matrix obtained in this way is used as a preconditioner. We analyze the distribution of the eigenvalues of the preconditioned matrix and the regularization properties. Numerical experiments, shown for the image restoration problem, validate the theoretical results. (C) 2004 Elsevier Ltd. All rights reserved.