Validated Numerics for Pedestrians

Abstract

The aim of this paper is to give a very brief introduction to the emerging area of validated numerics. This is a rapidly growing field of research faced with the challenge of interfacing computer science and pure mathematics. Most validated numerics is based on interval analysis, which allows its users to account for both rounding and discretization errors in computer-aided proofs. We will illustrate the strengths of these techniques by converting the well-known bisection method into a efficient, validated root finder.