## 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 ...