### 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 |

### Bibliographical note

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

- ODEs
- theorem proving
- validated numeric computation

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## 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). Springer. https://doi.org/10.1007/978-3-662-44199-2_101