Practical band Toeplitz preconditioning and boundary layer effects (Q1418861)

Band Toeplitz preconditioners are known to be optimal for Hermitian positive definite systems in the sense that the obtained convergence rate is independent of the size of the considered systems. The construction of such preconditioners requires the knowledge of the zeros of the underlying generating function. The paper provides conditions on the approximation error of these zeros determined within a given precision in order to maintain the optimality property, and numerical experiments are also presented.