IJPAM: Volume 76, No. 4 (2012)

SOFTWARE IMPLEMENTATION OF MODIFICATIONS OF
ITERATIVE ALGORITHMS FOR SOLVING
LINEAR SYSTEMS OF EQUATIONS

Angel Golev$^1$, Anna Malinova$^2$, Desislava Zaharieva$^3$
$^{1,2,3}$Faculty of Mathematics and Informatics
University of Plovdiv
236, Bulgaria Blvd., Plovdiv, 4003, BULGARIA


Abstract. This paper presents a software package developed in Mathematica that contains implementations of various, mostly proposed during the last three years, iterative algorithms, including combined algorithms, for solving linear systems of equations. The accent falls on algorithms of type successive overrelaxation which are modifications of the Gauss-Seidel algorithm (forward and reverse iteration), as well as newer modifications applicable to systems with iterative $M$-matrices. The package provides the algorithms' implementations, a set of functions that perform convergence analysis using criteria described in literature, and additional utility functions. Described are the iterative algorithms and the software implementation. A numerical example demonstrating the use of the developed package is also given.

Received: December 14, 2011

AMS Subject Classification: 65F10

Key Words and Phrases: solving linear systems of equations, iterative algorithms, Nekrassov-Mehmke algorithm (forward and reverse iteration), generalized Nekrassov-Mehmke algorithms, modifications of the Nekrassov-Mehmke algorithm, generalized accelerated over relaxation algorithms based on Nekrassov-Mehmke scheme, M-matrices, Mathematica package, parameterized template, code generation, rule-based programming, patterns, help documentation

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 76
Issue: 4