Three-part splittings and Varga's type extensions of the successive overrelaxation (SOR) theory

A. Hadjidimos

Mathematics and Computers in Simulation (MATCOM), 1980, vol. 22, issue 3, 242-247

Abstract: Varga, in his excellent book [4] and in a later paper of his [5], extended the SOR theory in various directions by having considered the well known Ostrowski-Reich theorem as a starting point. In this paper we extend the theory by considering three-part splittings of Varga's type, where one of the basic parts is negative definite instead of being positive definite. Thus we are able to construct SOR-type schemes which converge for all the values of the overrelaxation parameter ω which do not belong to the familiar interval [0,2]. Then by following a similar but more complicated analysis, than that in [5], we are able to obtain the corresponding optimum schemes in the various possible cases.

Date: 1980
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:22:y:1980:i:3:p:242-247

DOI: 10.1016/0378-4754(80)90051-8

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