An Application Of Matrices To Least Square Methods

In most problems in mathematics, science, engineering, and economics it is sufficient to find an equation which posses within certain distances of a given set of points; consequently, a selection of the equation form to he fitted to the points must be made. Our problem arises from an obvious need for a criteria to satisfy given empirical points to represent a function and find the most convenient matrix solution to the system of linear equations derived from our function. The fitting of empirical points by equations may be accomplished in two district manners. One is to have the equation satisfied exactly at the observational points, The other is to have the approximating function come as close as possible to numbers at the given points and still retain a predetermined characteristic which will show the general nature of the data but will not necessarily pass exactly through the given points, The Methods of Least Square, with our matrix solution, are designed to achieve this end. The notations and definitions will be given in Chapter I. The basic theorems to be used will be found in Chapter II. Chapter III will be devoted to a matrix solution of a polynomial of degree n through m distinct points in the plane. In Chapter IV, we will discuss a matrix solution of a plane through n distinct points. The least-square methods will be used to determine the curves in each of the above chapters. Applications of matrices solutions of a polynomial of degree n through m distinct points and a plane through n distinct points will be given in Chapter V. The summary will be given in Chapter VI followed by the bibliography