Abstract
This paper is concerned with the generalized accelerated overrelaxation (GAOR) method, which constitutes a generalization of the basic iterative methods for the solution of linear systems. A number of new theoretical results are presented concerning the convergence theory of the GAOR method and special cases of it. Much attention is given to linear systems with positive definite coefficient matrices. Although the problem of determining the various optimum parameters of the GAOR method in the general case is very difficult to solve theoretically and is still an open one, the numerical examples which are presented in this paper show that a suitable exploitation of it may give much better results than the other basic iterative methods.
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