Comparative Analysis of Numerical Solution to a Linear System of Algebraic Equations

Abstract

In engineering and science, linear systems of algebraic equations occur often as exact or approximate formulations of various problems. These types of equations are well represented in matrix form. A major challenge for researchers is the choice of algorithm to use for an appropriate solution. In this study, we choose to experiment with three algorithms for the solution to a system of linear algebraic equation. After subjecting the matrix form of the system of linear algebraic equations to the rank test, Gaussian Elimination method, Inverse Matrix Method and Row-Reduced Echelon were used to evaluate twenty-four (24) sets of solutions. Numerical methods are plagued by truncation and round-off errors thus, we choose to compute and compare result here by invoking the MATLAB command format long (15 decimal place) with format short (5 decimal place). After evaluating the required solutions, we substituted all computed results back into the system of linear algebraic equations to check if they are satisfied. Comparison of results was done on the basis of algorithm used and between the results obtained using either format long or format short values. Despite the presence of errors due to truncation and round-off, format short computed solutions gave acceptable result in some cases. Results obtained in this study proved the efficacy of the proposed technique.