Convergence for a general form of the GAOR method and its application to the MSOR method
The generalized accelerated overrelaxation iterative method with the iteration matrix \[ L_{R\Omega} = (D_ A - RE_ 0)^{-1}[(I - \Omega) D_ A + (\Omega - R)E_ 0 + QF_ 0] \] is considered for the solution of a linear system \(Ax = b\). Here, \(A = D_ A - E_ 0 - F_ 0\); \(D_ A\) is the diagonal part of \(A\); \(R\), \(\Omega\) are diagonal matrices. This GAOR method includes various generalizations of the well-known SOR method, as e.g. the modified successive overrelaxation (MSOR) method by \textit{D. M. Young} [Iterative solution of large linear systems (1971; Zbl 0231.65034)] and the methods presented by \textit{A. Hadjidimos} [Int. J. Comput. Math. 14, 355-369 (1983; Zbl 0517.65012)] and \textit{J. Hu} [Math. Numer. Sin. 13, No. 2, 142-144 (1991)]. New results are obtained for the convergence domain of \(L_{R\Omega}\) in the case when \(A\) is a complex \(H\)-matrix. These results have interesting consequences extending the convergence theory of the previously mentioned generalizations of the SOR method.
generalized accelerated overrelaxation iterative method
scientific article; zbMATH DE number 519704