Horner's rule for interval evaluation revisited

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

Research output: Contribution to journalArticle

15 Citations (Scopus)


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)
Issue number1
Publication statusPublished - 1 Jan 2002


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

ASJC Scopus subject areas

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

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  • Cite this

    Hartig, J. S., Najafi-Shoushtari, S. 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