Interval Analysis

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Abstract

Interval analysis is a calculus based on set-valued mathematics.In its simplest (and by far most popular) form, it builds upon interval arithmetic, which is a natural extension of real-valued arithmetic. Despite its simplicity, this kind of set-valued mathematics has a very wide range of applications in computer-aided proofs for continuous problems. In a nutshell, interval arithmetic enables us to bound the range of a continuous function, i.e., it produces a set enclosing the range of a given function over a given domain. This, in turn, enables us to prove mathematical statements that use open conditions, such as strict inequalities, fixed-point theorems, etc.
Original languageEnglish
Title of host publicationThe Princeton Companion to Applied Mathematics
EditorsNicholas J Higham, Mark R Dennis, Paul Glendinning, Paul A Martin, Fadil Santosa, Jared Tanner
Place of PublicationPrinceton NJ USA
PublisherPrinceton University Press
ChapterII.20
Pages105-106
Number of pages2
ISBN (Print)978-0-691-15039-0
Publication statusPublished - 2015
Externally publishedYes

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