  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.
