Successive overrelaxation (SOR) and related methods

Covering the last half of the 20th century, we present some of the basic and well-known results for the SOR theory and related methods as well as some that are not as well known. Most of the earlier results can be found in the excellent books by Varga (Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1962) Young (Iterative Solution of Large Linear systems, Academic Press, New York, 1971) and Berman and Plemmons (Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia, PA, 1994) while some of the most recent ones are given in the bibliography of this paper. In this survey, both the point and the block SOR methods are considered for the solution of a linear system of the form Ax=b, where A∈Cn,n and b∈Cn⧹{0}. Some general results concerning the SOR and related methods are given and also some more specific ones in cases where A happens to possess some further property, e.g., positive definiteness, L-, M-, H-matrix property, p-cyclic consistently ordered property etc.