ABSTRACT
In approximation theory, two general types of problems arise in fitting tabular data. The first one consists of finding an approximating function (perhaps a piecewise polynomial) that passes through every point in the table. The other problem consists of finding the “best” function that can be used to represent the data but does not exactly pass through every data point. This category of problems is called curve fitting and will be the subject of this chapter. In Chapter 5, we constructed polynomial approximations to tabular data using
interpolation methods. Interpolating polynomials are best used for approximating a function f whose values are known with high accuracy. Often, however, the tabulated data are known to be only approximate. More precisely, in most of the situations, data are given by a set of measurements having experimental errors. Hence, interpolation in this case is of little use, if not dangerous. Consider, for example, a simple physical experiment in which a spring is stretched from its equilibrium position by a known external force (see Figure 7.1).
