Abstract:
The Jacobi and Gauss-Seidel methods are among the basic iterative methods for solving system of
linear equations. They are now mostly used as pre conditioners for the popular iterative solvers. The
main purpose of this .report is to introduce the new method Known as "REFINEMENT OF
GENERALIZED GAUSS-SEIDEL ITERATION METHODS FOR SOLVING SYSTEM OF LINEAR
EQUATIONS" for solving linear systems of equations", Ax=b and discuss its convergence. This report is
divided in to two Chapters; the first chapter includes introduction and preliminarily which are used for
our subsequent discussion of the second chapter. In the second chapter, the derivation of the new method,
Refinement of Generalized Gauss Seidel (RGGS) iteration method is discussed thoroughly. Few
numerical examples are considered to show the efficiency of this new method over the GGS method and
other iterative methods in general.
