On the Gauss-Seidel's iteration method [Lecture]

D-iteration method or how to improve Gauss-Seidel method

The aim of this paper is to present the recently proposed fluid diffusion based algorithm in the general context of the matrix inversion problem associated to the Gauss-Seidel method. We explain the simple intuitions that are behind this diffusion method and how it can outperform existing methods. Then we present some theoretical problems that are associated to this representation as open resea...

On Algebraic Structure of Improved Gauss-Seidel Iteration

Analysis of real life problems often results in linear systems of equations for which solutions are sought. The method to employ depends, to some extent, on the properties of the coefficient matrix. It is not always feasible to solve linear systems of equations by direct methods, as such the need to use an iterative method becomes imperative. Before an iterative method can be employed to solve ...

An Extrapolated Gauss - Seidel Iteration for Hessenberg Matrices

We show that for certain systems of linear equations with coefficient matrices of Hessenberg form it is possible to use Gaussian elimination to obtain an extrapolated version of the Gauss-Seidel iterative process where the iteration matrix has spectral radius zero. Computational aspects of the procedure are discussed.

Gauss-Seidel Iteration for Stiff ODES from Chemical Kinetics

A simple Gauss-Seidel technique is proposed which exploits the special form of the chemical kinetics equations. Classical Aitken extrapolation is applied to accelerate convergence. The technique is meant for implementation in stii solvers that are used in long range transport air pollution codes using operator splitting. Splitting necessarily gives rise to a great deal of integration restarts. ...

Medical education: capitalizing on the lecture method.