Analysis of preconditioning techniques for ill-conditioned Toeplitz matrices

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.