ABSTRACT
As part of the intricate process of analyzing experimental data, one often has to plot the observed data points on a graph in order to determine whether some kind of mathematical relationship exists that can describe the observed results. The data points are usually plotted as a discrete set of N ordered pairs: (x0,y0),(x1,y1), . . . ,(xN ,yN) such that x0 < x1 < · · · < xN . Often the points are equally spaced but that is not always necessarily true. In any event, we know the value of the function yi = f (xi) at each data point but we don’t have a general analytic expression for f (x) that would allow us to calculate values at an arbitrary point (x,y). It would thus be highly desirable to be able to accurately estimate f (x) for arbitrary x. In some cases, this process will also allow us to draw a smooth curve through, and perhaps even beyond, the given set of data points. If the desired x value lies between the smallest and largest values of the given set of points (xi,yi), then the process is called interpolation. If x being sought is outside that given range, then the process is called extrapolation and the results are much less reliable, as many former stock market analysts can very likely attest.
