A note on superoptimal generalized circulant preconditioners

Circulant matrices can be effective preconditioners for linear systems of equations with a Toeplitz matrix. Several approaches to construct such preconditioners have been described in the literature. This paper focuses on the superoptimal circulant preconditioners proposed by Tyrtyshnikov, and investigates a generalization obtained by allowing generalized circulant matrices. Numerical examples illustrate that the new preconditioners so obtained can give faster convergence than available preconditioners based on circulant and generalized circulant matrices.