Preconditioning of block Toeplitz matrices by sine transforms

The iterative solution of a block Toeplitz linear system by the conjugate gradient method is analyzed, the preconditioning step being solved by means of a discrete sine transform. Convergence properties are established and compared to the behaviour of the block circulant preconditioner recently proposed in literature. As in the scalar case, the new approach takes advantage if the system is ill-conditioned.