Recent numerical experiments comparing successive overrelaxation iterative methods with implicit alternative direction iterative methods

Abstract

Recent theoretical advances in variants of both the successive overrelaxation iterative methods (such as the Golub-Varga cyclic Chebyshev semi-iterative method (196l) and the implicit alternating direction iterative methods (such as the Wachspress-Habetler normalized Peaceman-Rachford iterative method (1960))suggest extensions of the numerical experiments by Young and Ehrlich (1959) comparing these iterative methods. These experiments were carried out on the IBM-704 and 7090 for the set of problems originally considered by Young and Ehrlich, with the addition of a set of numerical problems encountered in the petroleum industry.