TABLE OF CONTENTS In this chapter we describe numerical methods for the approximation of functions other than elementary functions. The main purpose of these techniques is to replace a complicated function by one that is simpler and more manageable. We sometimes know the value of a function f ( x ) at a set of points (say, x 0< x 1< x 2 < x n) but we do not have an analytic expression for f ( x ) that lets us calculate its value at an arbitrary point. We concentrate on techniques that may be adapted if, for example, we have a table of values of functions that may have been obtained from some physical measurement or some experiments or long numerical calculations that cannot be cast into a simple functional form. The task now is to estimate f(x) for an arbitrary point x by, in some sense, drawing a smooth curve through (and perhaps beyond) the data point x i . If the desired x is in between the largest and smallest of the data point, then the problem is called interpolation; and if x is outside that range, it is called extrapolation. In this chapter we shall restrict our attention to interpolation. It is a rational process generally used in estimating a missing functional value by taking a weighted average of known functional values at neighboring data points.
An interpolation scheme must model the function...
