Abstract
In this paper we consider various iterative methods for solving systems of linear algebraic equations. We shall be primarily concerned with large systems with sparse matrices such as arise in the solution of elliptic boundary value problems in two dimensions by finite difference methods. Our discussion is divided into two parts: First, we review the well-known facts about such methods as the Jacobi, Gauss-Seidel, and successive overrelaxation methods. A treatment of various acceleration techniques is included. In the second part of the paper we consider the symmetric overrelaxation method and describe some practical procedures which can be used to obtain very rapid convergence. By showing that the method can be very effective in many cases and by outlining a definite procedure for its application, we hope to encourage its wider usage and to stimulate further research.
Work on this paper was supported in part by the U.S.Army Research Office (Durham), grant DA-ARO-D-31-124-734 at The University of Texas at Austin.
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© 1973 D. Reidel Publishing Company, Dordrecht
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Young, D.M. (1973). Solution of Linear Systems of Equations. In: Gram, J.G. (eds) Numerical Solution of Partial Differential Equations. Nato Advanced Study Institutes Series, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2672-7_3
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DOI: https://doi.org/10.1007/978-94-010-2672-7_3
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