Construction of New Iterative Method to Solve Linear Systems Using Generalized Inverse

Abstract

Numerical analysis constitutes the study, modification and analysis of methods explicitly which can’t be solved analytically. Applied field of engineering require extensive knowledge and detailed analysis for solving linear system of equations. Hence our basic and fundamental task is to determine and generate methods which help us in finding the solutions. Thus, the thesis presented here gives comprehensive view of various techniques required in study linear systems. The thesis consists of four chapter as follows: CHAPTER 1: This chapter constitutes basic definitions and concepts used in study of Linear algebra which are implemented in numerical techniques. Further, several techniques used for finding Moore-Penrose inverse are also included in light to solve real life engineering problems. CHAPTER 2: In this chapter assessment of different iterative schemes used to determine the generalized inverse of matrices are defined. The schemes are organized in their increasing order of convergence and their survey is being done. CHAPTER 3: The chapter contains a new iterative method for solving the system of linear equations. The concept has also been extended to Moore-Penrose inverse. The convergence criteria of proposed method along with detailed analysis is provided. CHAPTER 4: In this chapter numerical comparisons of new method with methods of same as well as different orders are provided. Some engineering applications have been provided for this purpose. The results and various factors related to problems are obtained using M athematica[11]