Analysis of Preconditioning Techniques for Ill-Conditioned Toeplitz Matrices

Abstract

Several preconditioning techniques for solving Toeplitz systems are known in literature, but their convergence features are completely understood only in the well-conditioned case. We study the application of $\tau $, circulant, and Hartley preconditioners to ill-conditioned Toeplitz matrices by proving that only the first class realizes a rate of convergence not depending on the dimension of the system.