Chapter

Perspectives on Enclosure Methods

pp 15-70

Advanced Arithmetic for the Digital Computer — Interval Arithmetic Revisited

  • Ulrich W. KulischAffiliated withInstitut für Angewandte Mathematik, Universität Karlsruhe (TH)

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Abstract

This paper deals with interval arithmetic and interval mathematics. Interval mathematics has been developed to a high standard during the last few decades. It provides methods which deliver results with guarantees. However, the arithmetic available on existing processors makes these methods extremely slow. The paper reviews a number of basic methods and techniques of interval mathematics in order to derive and focus on those properties which by today’s knowledge could effectively be supported by the computer’s hardware, by basic software, and by the programming languages. The paper is not aiming for completeness. Unnecessary mathematical details, formalisms and derivations are left aside whenever possible. Particular emphasis is put on an efficient implementation of interval arithmetic on computers.