COMPUTER APPROXIMATIONS.

Abstract

The objective of computer approximation is to calculate the value of a function to a given accuracy while expending as little computational energy as possible. Because of the various tricks that can be brought into play, this short article cannot present a cut-and-dried design technique. However, there is a small set of problems that have to be addressed in writing any numerical function routine. Each of these problems is discussed here in relation to a specific programming example. The main connecting theme is to design a program to compute the exponential function This leads into several interesting subplots. Considered are: round-off error, algorithm speed, range deduction, cancellation error, error amplification, approximation functions, polynomial approximations and rational approximations.