Error Analysis

Abstract

Input data as well as the results of elementary operations have to be represented by machine numbers, the subset of real numbers which is used by the arithmetic unit of today’s computers. Generally this generates rounding errors. This kind of numerical error can be avoided in principle by using arbitrary precision arithmetics or symbolic algebra programs. But this is unpractical in many cases due to the increase in computing time and memory requirements. Results from more complex operations like square roots or trigonometric functions can have even larger errors since series expansions have to be truncated and iterations accumulate the errors of the individual steps. In addition, the precision of input data from an experiment is limited. In this chapter we study the influence of numerical errors on the uncertainties of the calculated results and the stability of simple algorithms.