On Chebychev Acceleration Procedures for Alternating Direction Iterative Methods

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Abstract
The solution of large sparse systems of linear equations arising, for example, from the numerical solution of elliptic partial differential equations is considered, with reference to the acceleration technique commonly known as Chebychev acceleration. In particular its application to alternating direction iterative (A.D.I.) methods is compared with the more standard techniques such as successive overrelaxation. It is conjectured that in most circumstances a suitable A.D.I. strategy is that of applying Chebychev semiiteration to an A.D.I. process with a single A.D.I. parameter. It is shown that under general conditions this procedure may sometimes produce faster convergence than the usual multiparameter A.D.I. procedure.

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