Skip to main content

Interval Computations as Propagation of Constraints

  • Conference paper
Book cover Constraint Programming

Part of the book series: NATO ASI Series ((NATO ASI F,volume 131))

  • 150 Accesses

Abstract

Suppose that we have a program P written in some ordinary (i.e. nonconstraint) programming language which for given real inputs x 1,..., x n computes some real output y.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Baur W., Strassen V. (1983) The complexity of partial derivatives. Theor. Computer Sci. 22, 317–330

    Article  MathSciNet  MATH  Google Scholar 

  • Hansen E. (1975) A generalized interval arithmetic. Lecture Notes Computer Sci. 29, 7–18, Springer-Verlag, Berlin.

    Google Scholar 

  • Gaganov A. A. (1985) 0 slozhnosti vychisleniya intervala znachenii polynoma of mnogikh peremennykh. Kibernetika (Kiev) 4, (1985) 6–8; translation: Computational complexity of the range of a polynomial in several variables. Cybernetics 21, 418–421

    Google Scholar 

  • Iri M. (1991) History of automatic differentiation and rounding error estimation. In: A. Griewank, G. F. Corliss (eds.) Automatic Differentiation of Algorithms. Theory, Implementation, and Application, 3–16; common Automated Differentiation Bibliography collected by G. F. Corliss, 331–353. Philadelphia, SIAM

    Google Scholar 

  • Kaishev A.I. (1989) Updated scheme for construction of a posteriori interval extensions for elementary functions (in Russian). Voprosy Kibernetiki (Academy of Sciences of the USSR, Moscow) 149, 14–18

    MathSciNet  Google Scholar 

  • Kim K. V., Nesterov Yu. E., Cherkasskii B.V. (1984) Otsenka trudoemkosti vychisleniya gradienta. Doklady AN SSSR 275 (1984) 1306–1309; translation: An estimate of the efforts in computing the gradient. Soy. Math. Dokl. 29, 384–387

    MATH  Google Scholar 

  • Linnaimaa S. (1976) Taylor expansion of the accumulated rounding error. Bit 16, 146–160

    Article  Google Scholar 

  • Matijasevich. Yu. (1985) A posteriori interval analysis. Lecture Notes Computer Sci. 204, 328–334, Springer-Verlag, Berlin

    Google Scholar 

  • Matiyasevich Yu. (1986) Vetschestvennye chisla i ÉVM. In: V.A.Mel’nikov (ed.) Kibernetika i Vychislitel’naya technika 2, Nauka, Moscow, 104–133

    Google Scholar 

  • Moore R. E. (1966) Interval Analysis. Prentice Hall, Englewood Cliffs

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Matiyasevich, Y. (1994). Interval Computations as Propagation of Constraints. In: Mayoh, B., Tyugu, E., Penjam, J. (eds) Constraint Programming. NATO ASI Series, vol 131. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-85983-0_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-85983-0_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-85985-4

  • Online ISBN: 978-3-642-85983-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics