Original language | English |
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Title of host publication | The Princeton Companion to Applied Mathematics |

Editors | Nicholas J Higham, Mark R Dennis, Paul Glendinning, Paul A Martin, Fadil Santosa, Jared Tanner |

Place of Publication | Princeton NJ USA |

Publisher | Princeton University Press |

Chapter | II.20 |

Pages | 105-106 |

Number of pages | 2 |

ISBN (Print) | 978-0-691-15039-0 |

Publication status | Published - 2015 |

Externally published | Yes |

## Abstract

Interval analysis is a calculus based on set-valued mathematics.In its simplest (and by far most popular) form, it builds upon interval arithmetic, which is a natural extension of real-valued arithmetic. Despite its simplicity, this kind of set-valued mathematics has a very wide range of applications in computer-aided proofs for continuous problems. In a nutshell, interval arithmetic enables us to bound the range of a continuous function, i.e., it produces a set enclosing the range of a given function over a given domain. This, in turn, enables us to prove mathematical statements that use open conditions, such as strict inequalities, fixed-point theorems, etc.