Impact of Floating-Point Arithmetic on Engineering Numerical Analysis

Abstract

Floating-point number systems inevitably incur errors in representing both the input and the results of computation. Such errors can be minimized by careful selection and implementation of computational algorithms. Nevertheless, some problems are inherently sensitive (ill-conditioned) in that their solutions can change dramatically as a result of a small perturbation in their input, regardless of the algorithm used. On the other hand, poorly conceived algorithms can be numerically unstable in solving perfectly well conditioned problems. In backward error analysis, the accuracy of an approximate solution is assessed by determining a modified problem whose exact solution is the one actually obtained for the original problem. The objective of the paper is to review the floating-point number system and discuss its implications on the results of computations typical of those found in engineering numerical analysis.