On Generalized Jacobi, Gauss-Seidel and SOR Methods
Incremental extension of iterative methods for solving linear systems, providing new convergence results and a generalized SOR variant.
The paper studies generalized Jacobi and Gauss-Seidel methods, proposes a generalized SOR method, and demonstrates its advantages through numerical experiments with convergence criteria for various matrix classes.
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.