Function interval arithmetic

Jan Duracz, Amin Farjudian, Michal Konečný, Walid Taha

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish
Title of host publicationMathematical software – ICMS 2014
Subtitle of host publication4th international congress, Seoul, South Korea, August 5-9, 2014, proceedings
EditorsHoon Hong, Chee Yap
Place of PublicationBerlin (DE)
PublisherSpringer
Pages677-684
Number of pages8
ISBN (Electronic)978-3-662-44199-2
ISBN (Print)978-3-662-44198-5
DOIs
Publication statusPublished - 31 Dec 2014
Event4th International Congress on Mathematical Software - Seoul, Korea, Democratic People's Republic of
Duration: 5 Aug 20149 Aug 2014

Publication series

NameLecture Notes in Computer Science
PublisherSpringer
Volume8592
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Congress

Congress4th International Congress on Mathematical Software
Abbreviated titleICMS 2014
CountryKorea, Democratic People's Republic of
CitySeoul
Period5/08/149/08/14

Fingerprint

Interval Arithmetic
Hybrid Modeling
Theorem proving
Interval
Theorem Proving
Enclosure
Enclosures
Hybrid systems
Hybrid Systems
System Modeling
Ordinary differential equations
Numerical Computation
Ordinary differential equation
Software

Bibliographical note

Funding: EPSRC (EP/C01037X/1)

Keywords

  • ODEs
  • theorem proving
  • validated numeric computation

Cite this

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 (pp. 677-684). (Lecture Notes in Computer Science; Vol. 8592). Berlin (DE): Springer. https://doi.org/10.1007/978-3-662-44199-2_101
Duracz, Jan ; Farjudian, Amin ; Konečný, Michal ; Taha, Walid. / Function interval arithmetic. Mathematical software – ICMS 2014: 4th international congress, Seoul, South Korea, August 5-9, 2014, proceedings. editor / Hoon Hong ; Chee Yap. Berlin (DE) : Springer, 2014. pp. 677-684 (Lecture Notes in Computer Science).
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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; Taha, Walid.

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/Report/Conference proceedingConference contribution

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Duracz J, Farjudian A, Konečný M, Taha W. Function interval arithmetic. In Hong H, Yap C, editors, Mathematical software – ICMS 2014: 4th international congress, Seoul, South Korea, August 5-9, 2014, proceedings. Berlin (DE): Springer. 2014. p. 677-684. (Lecture Notes in Computer Science). https://doi.org/10.1007/978-3-662-44199-2_101