LSIterativeMethods

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 systems of linear 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.