For the solution of the linear system x = Tx + c (1), where T is weakly cyclic of index k ≥ 2, the block SOR method together with two classes of monoparametric k-step iterative Euler methods, whose (optimum) convergence properties were studied in earlier papers, are considered. By establishing...

In this work we consider the Helmholtz equation in a hyperparallelepiped Ω⊂Rd, d=1,2,3,…, under Dirichlet boundary conditions and for its solution we apply the averaging technique of the nonoverlapping Domain Decomposition, where Ω is decomposed in two, in general not equal, subdomains....

In this paper the construction of a stationary second order scheme of de Phillis' type, with optimal convergence rates, for the solution of a linear system is presented. Numerical tests have shown that the new scheme compares favorably with the very fast nonstationary second order one proposed...

This paper extends the theory of the Accelerated Overrelaxation (AOR) method and presents what is called Symmetric AOR (SAOR) method. This is done in a way analogous to the one where the SSOR method is obtained from the SOR one. In addition the theoretical and computational results which are...

The convergence rate of a numerical procedure based on Schwarz Alternating Method (SAM) for solving elliptic boundary value problems (BVPs) depends on the selection of the so-called interface conditions applied on the interior boundaries of the overlapping subdomains. It has been observed that...

Varga, in his excellent book [4] and in a later paper of his [5], extended the SOR theory in various directions by having considered the well known Ostrowski-Reich theorem as a starting point. In this paper we extend the theory by considering three-part splittings of Varga's type, where one of...

In this paper the authors extend the matrix quadrant factorisation techniques which are so applicable for parallel computers to include banded symmetric and centrosymmetric linear systems with a corresponding improvement in computational efficiency.