A New Algorithm for Solution of System of Linear Equations

Abstract

Systems of linear equations are used in a variety of fields. The canonical problem of solving a system of linear equations arises in numerous contexts in information theory, communication theory, and related fields. This thesis is aimed at analyzing the available methods for solving a system of linear equations of the form n x n. Using a couple of iterative and/or direct methods, implement a program for these methods that could be run for different dimension size n of system of linear equation . At the end, a graph can be plotted with time taken for execution of a method considered V/s dimension size n. In this contribution, we develop a solution that does not involve direct matrix inversion. The iterative nature of our approach allows for a distributed message-passing implementation of the solution algorithm. We present test results which show that our solver achieves good results, both in terms of numerical accuracy as well as computing time. Furthermore, even very large systems (n 1000) can be solved given a cluster with sufficient resources. We also address some properties of the algorithm, including convergence, exactness, its complexity order and relation to classical solution methods.