We propose several circulant preconditioners for systems defined by some functions $g$ of Toeplitz matrices $A_n$. In this paper we are interested in solving $g(A_n)\mathbf{ x}=\mathbf{ b}$ by the preconditioned conjugate method or the preconditioned minimal residual method, namely in the cases when $g(z)$ are the functions $e^{ z}$, $\sin{ z}$ and $\cos{ z}$. Numerical results are given to show the effectiveness of the proposed preconditioners.
Categories: math.NA