### Abstract

Interval arithmetic can be used to enclose the range of a real function over a domain. However, due to some weak properties of interval arithmetic, a computed interval can be much larger than the exact range. This phenomenon is called dependency problem. In this paper, Horner's rule for polynomial interval evaluation is revisited. We introduce a new factorization scheme based on well-known symbolic identities in order to handle the dependency problem of interval arithmetic. The experimental results show an improvement of 25% of the width of computed intervals with respect to Homer's rule.

Original language | English |
---|---|

Pages (from-to) | 51-81 |

Number of pages | 31 |

Journal | Computing (Vienna/New York) |

Volume | 69 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2002 |

Externally published | Yes |

### Fingerprint

### Keywords

- Factorization
- Interval arithmetic
- Interval evaluation
- Polynomial expression
- Symbolic forms

### ASJC Scopus subject areas

- Theoretical Computer Science
- Software
- Numerical Analysis
- Computer Science Applications
- Computational Theory and Mathematics
- Computational Mathematics

### Cite this

*Computing (Vienna/New York)*,

*69*(1), 51-81. https://doi.org/10.1007/s00607-002-1448-y

**Horner's rule for interval evaluation revisited.** / Hartig, Jörg S.; Najafi, Hani; Grüne, Imke; Yan, Amy; Ellington, Andrew D.; Famulok, Michael.

Research output: Contribution to journal › Article

*Computing (Vienna/New York)*, vol. 69, no. 1, pp. 51-81. https://doi.org/10.1007/s00607-002-1448-y

}

TY - JOUR

T1 - Horner's rule for interval evaluation revisited

AU - Hartig, Jörg S.

AU - Najafi, Hani

AU - Grüne, Imke

AU - Yan, Amy

AU - Ellington, Andrew D.

AU - Famulok, Michael

PY - 2002

Y1 - 2002

N2 - Interval arithmetic can be used to enclose the range of a real function over a domain. However, due to some weak properties of interval arithmetic, a computed interval can be much larger than the exact range. This phenomenon is called dependency problem. In this paper, Horner's rule for polynomial interval evaluation is revisited. We introduce a new factorization scheme based on well-known symbolic identities in order to handle the dependency problem of interval arithmetic. The experimental results show an improvement of 25% of the width of computed intervals with respect to Homer's rule.

AB - Interval arithmetic can be used to enclose the range of a real function over a domain. However, due to some weak properties of interval arithmetic, a computed interval can be much larger than the exact range. This phenomenon is called dependency problem. In this paper, Horner's rule for polynomial interval evaluation is revisited. We introduce a new factorization scheme based on well-known symbolic identities in order to handle the dependency problem of interval arithmetic. The experimental results show an improvement of 25% of the width of computed intervals with respect to Homer's rule.

KW - Factorization

KW - Interval arithmetic

KW - Interval evaluation

KW - Polynomial expression

KW - Symbolic forms

UR - http://www.scopus.com/inward/record.url?scp=0036387347&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036387347&partnerID=8YFLogxK

U2 - 10.1007/s00607-002-1448-y

DO - 10.1007/s00607-002-1448-y

M3 - Article

VL - 69

SP - 51

EP - 81

JO - Computing (Vienna/New York)

JF - Computing (Vienna/New York)

SN - 0010-485X

IS - 1

ER -