Function interval arithmetic

Jan Duracz, Amin Farjudian, Michal Konečný, Walid Taha

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


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)
Number of pages8
ISBN (Electronic)978-3-662-44199-2
ISBN (Print)978-3-662-44198-5
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
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Congress4th International Congress on Mathematical Software
Abbreviated titleICMS 2014
CountryKorea, Democratic People's Republic of

Bibliographical note

Funding: EPSRC (EP/C01037X/1)


  • ODEs
  • theorem proving
  • validated numeric computation

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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 (pp. 677-684). (Lecture Notes in Computer Science; Vol. 8592). Springer.