Engineering Mathematics, Volume 2

5

Curve Fitting

5.1 Introduction

The data obtained through measurement or observation may be plotted graphically, and a smooth curve is drawn joining the data points. Such graph is called an approximating curve for the data. The process of finding a curve that is “a best fit” for given data is called curve fitting. Several methods exist for curve fitting. We consider, in this chapter, curve fitting by a sum of exponential, linear/nonlinear weighted least squares approximation methods.

5.1.1 Curve Fitting: Method of Least Squares

So far we have employed polynomial interpolation where we have replaced the unknown function y = f(x) by a polynomial of degree at most n such that

 

f(x_i) = p_n (x_i) (i = 0, 1, 2, …. n)            (5.1)

 

This gives satisfactory ...