Horner's rule for interval evaluation revisited

Jörg S. Hartig, Hani Najafi, Imke Grüne, Amy Yan, Andrew D. Ellington, Michael Famulok

Research output: Contribution to journalArticle

12 Citations (Scopus)

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 languageEnglish
Pages (from-to)51-81
Number of pages31
JournalComputing (Vienna/New York)
Volume69
Issue number1
DOIs
Publication statusPublished - 2002
Externally publishedYes

Fingerprint

Interval Arithmetic
Factorization
Polynomials
Interval
Evaluation
Range of data
Polynomial
Experimental Results

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

Hartig, J. S., Najafi, H., Grüne, I., Yan, A., Ellington, A. D., & Famulok, M. (2002). Horner's rule for interval evaluation revisited. 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.

In: Computing (Vienna/New York), Vol. 69, No. 1, 2002, p. 51-81.

Research output: Contribution to journalArticle

Hartig, JS, Najafi, H, Grüne, I, Yan, A, Ellington, AD & Famulok, M 2002, 'Horner's rule for interval evaluation revisited', Computing (Vienna/New York), vol. 69, no. 1, pp. 51-81. https://doi.org/10.1007/s00607-002-1448-y
Hartig, Jörg S. ; Najafi, Hani ; Grüne, Imke ; Yan, Amy ; Ellington, Andrew D. ; Famulok, Michael. / Horner's rule for interval evaluation revisited. In: Computing (Vienna/New York). 2002 ; Vol. 69, No. 1. pp. 51-81.
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