A Refinement of some Overrelaxation Algorithms for Solving a System of Linear Equations
DOI:
https://doi.org/10.55630/sjc.2013.7.245-256Keywords:
reverse Gauss–Seidel method, or Nekrassov–Mehmke 2 method – (NM2), Successive Overrelaxation method with 1 parameter, based on (NM2) – (SOR1NM2), Successive Overrelaxation method with 2 parameters, based on (NM2) – (SOR2NM2), Refinement of (SOR1NM2)Abstract
In this paper we propose a refinement of some successive overrelaxation methods based on the reverse Gauss–Seidel method for solving a system of linear equations Ax = b by the decomposition A = Tm − Em − Fm, where Tm is a banded matrix of bandwidth 2m + 1. We study the convergence of the methods and give software implementation of algorithms in Mathematica package with numerical examples.
ACM Computing Classification System (1998): G.1.3.
