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Enclosure Methods Institut fr Angewandte Mathematik

Summary: Enclosure Methods
G. Alefeld
Institut für Angewandte Mathematik
Universität Karlsruhe
Federal Republic of Germany
Abstract: We present an overview on existing methods for inc1uding the range of
functions by interval arithmetic tools.
1. Introduction
In this paper we do not try to give a precise definition oEwhat we mean by an
enclosure method. Instead we first recall that the four basic interval operations
allow to inc1ude the range of values oErational Eunctions.Using more appropriate
tools also the range oEmore general functions can be included. Since all enclosure
methods for the solution of equations which are based on interval arithrnetic tools
are finally enc10sure methods for the range of some function we concentrate our-
selves on rnethods fo~ the inc1usion oEthe range oEfunctions. We limit our dis-
cussion to the case oEfunctions oEone real variable. Most oE the material in the
present paper is weIl known. See [1], Chapter 3 and the books [9], [10] by
Ratschek and Rokne, for example. However, there are also some new results. See
Theorem 2, for example.
Computer Arithmetic and Self-Validating


Source: Alefeld, Götz - Institut für Angewandte und Numerische Mathematik & Fakultät für Mathematik, Universität Karlsruhe


Collections: Mathematics