A Unique Approach to Solve the System of Linear Equations

Abstract

System of linear equations is a set of linear equations with same types of variables. Aside from mathematics, systems of linear equations are used in information theory, communication theory, and related fields. This study is aimed at analyzing the available methods and develops a new solution which does not involve direct matrix inversion for system of linear equations. By comparing the different test results with an existing and very well-known method called gauss elimination method, it has been seen that in terms of numerical accuracy and computing time the proposed approach achieves improve results. Furthermore, even very large systems can be solved by this proposed algorithm given a cluster with sufficient resources.