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Regular splittings and the discrete Neumann problem

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Summary

Iterative methods are discussed for approximating a solution to a singular but consistent square linear systemAx=b. The methods are based upon splittingA=M−N withM nonsingular. Monotonicity and the concept of regular splittings, introduced by Varga, are used to determine some necessary and some sufficient conditions in order that the iterationx i+1=M−1Nxi+M−1b converge to a solution to the linear system. Finally, applications are given to solving the discrete Neumann problem by iteration which are based upon the inherent monotonicity in the formulation.

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Authors and Affiliations

  1. Computer Science Dept., University of Tennesee, 37916, Knoxville, Tenn., USA

    R. J. Plemmons

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  1. R. J. Plemmons
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This research was supported by the U. S. Army Research Office-Durham under contract no. DAHCO4 74 C 0019.

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Plemmons, R.J. Regular splittings and the discrete Neumann problem. Numer. Math. 25, 153–161 (1976). https://doi.org/10.1007/BF01462269

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