On Generalized Jacobi, Gauss-Seidel and SOR Methods

TL;DR

This paper extends classical iterative methods like Jacobi, Gauss-Seidel, and SOR, providing new convergence criteria and demonstrating their advantages through numerical experiments for different matrix classes.

Contribution

It introduces a generalized SOR method with proven convergence properties and compares it to existing methods, enhancing iterative solution techniques.

Findings

Generalized methods have broader convergence criteria.

Numerical experiments show improved performance.

Advantages over classical methods are established.

Abstract

In this paper generalization of Jacobi and Gauss-Seidel methods, introduced by Salkuyeh in 2007, is studied. In particular, convergence criteria for these methods are discussed. A generalization of successive overrelaxation~(SOR) method is proposed, and its convergence properties for various classes of matrices are discussed. Advantages of generalized SOR method are established through numerical experiments.