Interval Analysis

Warwick Tucker

Interval Analysis

Warwick Tucker

Research output: Chapter in Book/Report/Conference proceeding › Encyclopaedia / Dictionary Entry › Other › peer-review

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 language	English
Title of host publication	The Princeton Companion to Applied Mathematics
Editors	Nicholas J Higham, Mark R Dennis, Paul Glendinning, Paul A Martin, Fadil Santosa, Jared Tanner
Place of Publication	Princeton NJ USA
Publisher	Princeton University
Chapter	II.20
Pages	105-106
Number of pages	2
ISBN (Print)	9780691150390
Publication status	Published - 2015
Externally published	Yes

Cite this

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title = "Interval Analysis",

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.",

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booktitle = "The Princeton Companion to Applied Mathematics",

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TY - CHAP

T1 - Interval Analysis

AU - Tucker, Warwick

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

M3 - Encyclopaedia / Dictionary Entry

SN - 9780691150390

SP - 105

EP - 106

BT - The Princeton Companion to Applied Mathematics

A2 - Higham, Nicholas J

A2 - Dennis, Mark R

A2 - Glendinning, Paul

A2 - Martin, Paul A

A2 - Santosa, Fadil

A2 - Tanner, Jared

PB - Princeton University

CY - Princeton NJ USA

ER -