Abstract
This chapter discussess the convergence properties of second-degree methods and presents a direct comparison with the corresponding semi-iterative methods. By the use of a second-degree method one is able to accelerate the convergence of any iterative method with real eigenvalues, which are less than unity by an amount comparable to that attainable by using the optimum. It does not seem to be generally recognized that in many cases, in particular for the symmetric successive overrelaxation(SSOR)–stationary iterative method, a semi-iterative method can be replaced by a stationary second-degree method without a significant loss in convergence speed. It is possible that though this simplification is perhaps more apparent than real, it might lead to a more serious consideration of the SSOR method as a practical procedure in some cases.
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