paper

Optimal preconditioners for systems defined by functions of Toeplitz matrices

arXiv:1802.03622 · doi:10.1016/j.laa.2018.03.003

Abstract

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 $g (A_{n}) x = b$ 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.