The Singular Value Decomposition (SVD) For Solving a System Of Algebraic Equations

Abstract

In thesis we present an iterative method to solve a system of equations approximately. Firstly we use two iterative methods for the solutions of a system of algebraic equations namely Gauss Jacobi iteration method and Gauss-Siedel iteration method. Most the iterative methods may converge or not. However certain class of systems of simultaneous equations which is diagonally dominant do always converge to a solution using Gauss-Siedel method. It is possible that a system of equation might be diagonally dominant if we exchanges the equations with each other. Also, we presented the singular value decomposition(SVD). It has been used to determine the properties of matrix, matrix norm and rank. Since the inverse of a matrix is often di cult to compute accurately,the SVD is used to compute the matrix inverse and then solving a linear systems of equations. Also, we use the SVD method to solve one of the least squares problems which is overdetermined problem. We use the MATLAB software for the solution.