Solution of Toeplitz normal equations by sine transform based preconditioning

The normal equations constructed by a Toeplitz matrix are studied, in order to find a suitable preconditioner related to the discrete sine transform. New results are given about the structure of the product of two Toeplitz matrices, which allow the CGN method to achieve a superlinear rate of convergence. This preconditioner outperforms the circulant one for the iterative solution of Toeplitz least-squares problems; such strategy can also be applied to nonsymmetric linear systems. A block generalization is discussed.