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 |
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Title of host publication | Mathematical Software, ICMS 2014 - 4th International Congress, Proceedings |
Publisher | Springer Verlag |
Pages | 677-684 |
Number of pages | 8 |
ISBN (Print) | 9783662441985 |
DOIs | |
Publication status | Published - 2014 |
Externally published | Yes |
Event | 4th International Congress on Mathematical Software, ICMS 2014 - Seoul, Korea, Republic of Duration: 5 Aug 2014 → 9 Aug 2014 |
Publication series
Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 8592 LNCS |
ISSN (Print) | 0302-9743 |
ISSN (Electronic) | 1611-3349 |
Conference
Conference | 4th International Congress on Mathematical Software, ICMS 2014 |
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Country/Territory | Korea, Republic of |
City | Seoul |
Period | 5/08/14 → 9/08/14 |
Bibliographical note
Funding Information:This work was supported by EPSRC grant EP/C01037X/1, Altran Technologies SA, the US NSF CPS award 1136099 and Swedish KK-Foundation CERES Centre.
Keywords
- ODEs
- Theorem Proving
- Validated Numeric Computation
ASJC Scopus subject areas
- Theoretical Computer Science
- General Computer Science