THEMATIC SECTION: RESULT-VERIFYING COMPUTING Introduction

Suppose that after a lengthy computation the computer gives you some real number, and you want to be sure that this number is the correct result, or at least close to it. Or you need to know whether the problem (a nonlinear system, a differential equation, etc.) has a solution at all and where the solution(s) may be, or how much the results can vary if there are tolerances in the input. In this thematic section we focus on result-verifying algorithms based on interval arithmetic, a computational tool that might help you to answer such questions in an automated way. Some central ideas underlying interval arithmetic can be explained on a few pages; we will do so in the following. The obvious approaches will, however, often yield results that cannot be used in practice. Then more sophisticated techniques are required. We will give a few hints on how such techniques work. The interested reader is referred to books, e.g. [3, 5] or the “classics” [1, 4], for a broader introduction to interval arithmetic.