On the generalisation of the basic iterative methods for the solution of linear systems

Abstract

For the solution of the linear system Ax=b many iterative methods based on a splitting of A exist. Among them the Jacobi, the Gauss-Seidel and the Successive Overrelaxation (SOR) methods as well as their extrapolated counterparts are the most popular. This paper presents a new general method such that the aforementioned methods become special cases of it. Besides its four degrees of freedom, which make it a very flexible method, another of its main characteristics is that it is well-defined even when some elements on the diagonal of A are zero. The first results concerning the new method show that a proper exploitation of its basic properties will make it a very powerful technique.

Keywords:

• Linear system
• Iterative method
• Splitting
• Jacobi method
• Gauss- seidel method
• Successive overrelaxation (SOR) method
• Extrapolated method

C.R. Categories:

• 5.14