Zweiparametrige Überrelaxation

Summary A generalization of the method of successive overrelaxation (SOR-method) toward the solution ofx=A x+b (the matrixA being of a special form) is treated. The method depends on two parameters instead of one but needs no more computational efforts. For matricesA with real and pure imaginary eigenvalues, those parameters are determined for which the method converges and those which give fastest convergence. The class of matricesA yielding convergence is enlarged in comparison to the SOR-method. The convergence is speeded up except in some cases. Three numerical examples are presented.