Approximation by the Method of Least Square

Abstract

Numerical analysis is concerned with developing methods to find approximate solutions for scientific problems, these methods are used extensively to treat commercial and industrial problems. The problem is first put in a mathematical model, in a form that describes the behavior of the variables, after applying particular relations between them. In this thesis we study some methods in approximation theory. There are several reasons for studying approximation theory and methods, ranging from a need to represent functions in computer calculations to an interest in the mathematics of the subject. Although approximation algorithms are used through out the science and in many industrial and commercial fields, some of the theory has became highly specialized and abstract. Work in numerical analysis and in mathematical s oflware is the o ne of the main links between these two extremes, for it’s purpose is to provide computer users with the efficient programs for general approximation calculations, in order that useful advances in the subject can be applied. This work presents methods using polynomials to approximate a given function or a given discrete data. The work shows many approximation methods, begining with graphical methods, and the methods of average briefly, then the method of least square is given in more details and it is the main topic of this thesis. Some programs are designed to solve general problems in discrete least square problems, and special problems in continuous one.