Function interval arithmetic

Jan Duracz; Amin Farjudian; Michal Konečný; Walid Taha

doi:10.1007/978-3-662-44199-2_101

Function interval arithmetic

Jan Duracz, Amin Farjudian, Michal Konečný, Walid Taha

Computer Science Research Group

Research output: Chapter in Book/Published conference output › Conference publication

Abstract

We propose an arithmetic of function intervals as a basis for convenient rigorous numerical computation. Function intervals can be used as mathematical objects in their own right or as enclosures of functions over the reals. We present two areas of application of function interval arithmetic and associated software that implements the arithmetic: (1) Validated ordinary differential equation solving using the AERN library and within the Acumen hybrid system modeling tool. (2) Numerical theorem proving using the PolyPaver prover.

Original language	English
Title of host publication	Mathematical software – ICMS 2014
Subtitle of host publication	4th international congress, Seoul, South Korea, August 5-9, 2014, proceedings
Editors	Hoon Hong, Chee Yap
Place of Publication	Berlin (DE)
Publisher	Springer
Pages	677-684
Number of pages	8
ISBN (Electronic)	978-3-662-44199-2
ISBN (Print)	978-3-662-44198-5
DOIs	https://doi.org/10.1007/978-3-662-44199-2_101
Publication status	Published - 31 Dec 2014
Event	4th International Congress on Mathematical Software - Seoul, Korea, Democratic People's Republic of Duration: 5 Aug 2014 → 9 Aug 2014

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
Volume	8592
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Congress

Congress	4th International Congress on Mathematical Software
Abbreviated title	ICMS 2014
Country/Territory	Korea, Democratic People's Republic of
City	Seoul
Period	5/08/14 → 9/08/14

Bibliographical note

Funding: EPSRC (EP/C01037X/1)

Keywords

ODEs
theorem proving
validated numeric computation

Access to Document

10.1007/978-3-662-44199-2_101

Cite this

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title = "Function interval arithmetic",

abstract = "We propose an arithmetic of function intervals as a basis for convenient rigorous numerical computation. Function intervals can be used as mathematical objects in their own right or as enclosures of functions over the reals. We present two areas of application of function interval arithmetic and associated software that implements the arithmetic: (1) Validated ordinary differential equation solving using the AERN library and within the Acumen hybrid system modeling tool. (2) Numerical theorem proving using the PolyPaver prover.",

keywords = "ODEs, theorem proving, validated numeric computation",

author = "Jan Duracz and Amin Farjudian and Michal Kone{\v c}n{\'y} and Walid Taha",

note = "Funding: EPSRC (EP/C01037X/1); 4th International Congress on Mathematical Software, ICMS 2014 ; Conference date: 05-08-2014 Through 09-08-2014",

year = "2014",

month = dec,

day = "31",

doi = "10.1007/978-3-662-44199-2_101",

language = "English",

isbn = "978-3-662-44198-5",

series = "Lecture Notes in Computer Science",

publisher = "Springer",

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editor = "Hoon Hong and Chee Yap",

booktitle = "Mathematical software – ICMS 2014",

address = "Germany",

}

Duracz, J, Farjudian, A, Konečný, M & Taha, W 2014, Function interval arithmetic. in H Hong & C Yap (eds), Mathematical software – ICMS 2014: 4th international congress, Seoul, South Korea, August 5-9, 2014, proceedings. Lecture Notes in Computer Science, vol. 8592, Springer, Berlin (DE), pp. 677-684, 4th International Congress on Mathematical Software, Seoul, Korea, Democratic People's Republic of, 5/08/14. https://doi.org/10.1007/978-3-662-44199-2_101

Function interval arithmetic. / Duracz, Jan; Farjudian, Amin; Konečný, Michal et al.
Mathematical software – ICMS 2014: 4th international congress, Seoul, South Korea, August 5-9, 2014, proceedings. ed. / Hoon Hong; Chee Yap. Berlin (DE): Springer, 2014. p. 677-684 (Lecture Notes in Computer Science; Vol. 8592).

Research output: Chapter in Book/Published conference output › Conference publication

TY - GEN

T1 - Function interval arithmetic

AU - Duracz, Jan

AU - Farjudian, Amin

AU - Konečný, Michal

AU - Taha, Walid

N1 - Funding: EPSRC (EP/C01037X/1)

PY - 2014/12/31

Y1 - 2014/12/31

N2 - We propose an arithmetic of function intervals as a basis for convenient rigorous numerical computation. Function intervals can be used as mathematical objects in their own right or as enclosures of functions over the reals. We present two areas of application of function interval arithmetic and associated software that implements the arithmetic: (1) Validated ordinary differential equation solving using the AERN library and within the Acumen hybrid system modeling tool. (2) Numerical theorem proving using the PolyPaver prover.

AB - We propose an arithmetic of function intervals as a basis for convenient rigorous numerical computation. Function intervals can be used as mathematical objects in their own right or as enclosures of functions over the reals. We present two areas of application of function interval arithmetic and associated software that implements the arithmetic: (1) Validated ordinary differential equation solving using the AERN library and within the Acumen hybrid system modeling tool. (2) Numerical theorem proving using the PolyPaver prover.

KW - ODEs

KW - theorem proving

KW - validated numeric computation

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UR - http://link.springer.com/chapter/10.1007%2F978-3-662-44199-2_101

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DO - 10.1007/978-3-662-44199-2_101

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AN - SCOPUS:84905860698

SN - 978-3-662-44198-5

T3 - Lecture Notes in Computer Science

SP - 677

EP - 684

BT - Mathematical software – ICMS 2014

A2 - Hong, Hoon

A2 - Yap, Chee

PB - Springer

CY - Berlin (DE)

T2 - 4th International Congress on Mathematical Software

Y2 - 5 August 2014 through 9 August 2014

ER -

Function interval arithmetic

Abstract

Publication series

Congress

Bibliographical note

Keywords

Access to Document

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Cite this