The Preconditioned Gauss-Seidel Method

Hiroshi Niki, Hiroyuki Hirano and Toshiyuki Kohno

preconditioning, Gauss-Seidel
In this paper, we consider the iterative method with the preconditioner $(I+\beta U)$ where $\beta$ is a positive parameter. We propose the new technique to estimate the optimum parameter $\beta=1+\rho$ by using Neumann's expansion for approximation of $A^{-1}$. It is shown with the numerical result that this method is superior to other methods.
the 16th IMACS (the International Association for Mathematics and Computers in Simulation) World Congress 2000 on Scientific Computation, Applied Mathematics and Simulation

Proceedings of the 16th IMACS  World Congress 2000 on Scientific Computation, Applied Mathematics and Simulation, pp.1-6(CD-ROM)