On an SSOR matrix relationship and its consequences

Abstract

AbstractA matrix relationship connecting the Jacobi and the Symmetric Successive Overrelaxation (SSOR) matrices associated with a k‐cyclic consistently ordered matrix A is presented. Next the equivalence of the SSOR method and a certain monoparametric k‐step one for the solution of the linear algebraic system Ax = b is established. The aforementioned equivalence can be exploited to derive regions of convergence, optimum parameters involved, etc. of the two iterative methods above. This is done by studying the simplest of the two methods that is the monoparametric k‐step one. To show how the idea works the case k = 2 is very briefly discussed.