On complex extrapolated successive overrelaxation (esor) : some theoretical results

摘要

In this paper we discuss the complex theory of the extrapolated successive overrelaxation (ESOR) method for the numerical solution of large sparse linear systems A · x = b of complex algebraic equations. Some subsets of convergence for this method are obtained through an application of conformal mapping techniques. We also study the choice of the involved complex parameters giving an arbitrarily "good" convergence behavior for the method. Among other results, it is shown that in general there is no value of the complex parameters maximizing the asymptotic rate of convergence and we investigate the conditions under which the complex extrapolated Gauss-Seidel (EGS) method converges as soon as possible.