### 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 |

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 | |

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 |
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Publisher | Springer |

Volume | 8592 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Congress

Congress | 4th International Congress on Mathematical Software |
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Abbreviated title | ICMS 2014 |

Country | Korea, Democratic People's Republic of |

City | Seoul |

Period | 5/08/14 → 9/08/14 |

### Fingerprint

### Bibliographical note

Funding: EPSRC (EP/C01037X/1)### Keywords

- ODEs
- theorem proving
- validated numeric computation

### Cite this

*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

}

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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

UR - http://www.scopus.com/inward/record.url?scp=84905860698&partnerID=8YFLogxK

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

U2 - 10.1007/978-3-662-44199-2_101

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

M3 - Conference contribution

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)

ER -