this paper deals with scrutinizing the convergence properties of iterative methods to solve linear system of equations. recently, several types of the preconditioners have been applied for ameliorating the rate of convergence of the accelerated overrelaxation (aor) method. in this paper, we study the applicability of a general class of the preconditioned iterative methods under certain conditio...

Scientiic codes which use iterative methods are often diicult to parallelize well. Such codes usually contain while loops which iterate until they converge upon the solution. Problems arise since the number of iterations cannot be determined at compile time, and tests for termination usually require a global reduction and an associated barrier. We present a method which allows us avoid performi...

posed on a finite dimensional Hilbert space V ∼= R equipped with an inner product (·, ·). Here A : V 7→ V is an symmetric and positive definite (SPD) operator, f ∈ V is given, and we are looking for u ∈ V such that (1) holds. The direct method to solve (1) is to form A−1 or the action of A−1. For example, the Gaussian elimination or LU factorization still remains the most commonly used methods ...

New explicit group S.O.R. methods suitable for use on an asynchronous MIMD computer are presented for the numerical solution of the sparse linear systems derived from the discretization of two-dimensional , second-order, elliptic boundary value problems. A comparison with existing implicit line S.O.R. schemes for the Dirichlet model problem shows the new schemes to be superior (Barlow and Evans...

in this paper‎, ‎we study convergence behavior of the global fom (gl-fom) and global gmres (gl-gmres) methods for solving the matrix equation $axb=c$ where $a$ and $b$ are symmetric positive definite (spd)‎. ‎we present some new theoretical results of these methods such as computable exact expressions and upper bounds for the norm of the error and residual‎. ‎in particular‎, ‎the obtained upper...

In this paper, an interpolation method for solving linear diierential equations was developed using multiquadric scheme. Unlike most iterative formula , this method provides a global interpolation formulae for the solution. Numerical examples show that this method ooers a higher degree of accuracy than Runge-Kutta formula and the iterative multistep methods developed by Hyman (1978).