Advertisement

Interval Computations as Propagation of Constraints

  • Yuri Matiyasevich
Conference paper
Part of the NATO ASI Series book series (NATO ASI F, volume 131)

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.

Keywords

Partial Derivative Steklov Institute Arithmetical Operation Interval Arithmetic Interval Computation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baur W., Strassen V. (1983) The complexity of partial derivatives. Theor. Computer Sci. 22, 317–330MathSciNetCrossRefMATHGoogle Scholar
  2. Hansen E. (1975) A generalized interval arithmetic. Lecture Notes Computer Sci. 29, 7–18, Springer-Verlag, Berlin.Google Scholar
  3. 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, 418–421Google Scholar
  4. 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, SIAMGoogle Scholar
  5. 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, 14–18MathSciNetGoogle Scholar
  6. 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, 384–387MATHGoogle Scholar
  7. Linnaimaa S. (1976) Taylor expansion of the accumulated rounding error. Bit 16, 146–160CrossRefGoogle Scholar
  8. Matijasevich. Yu. (1985) A posteriori interval analysis. Lecture Notes Computer Sci. 204, 328–334, Springer-Verlag, BerlinGoogle Scholar
  9. Matiyasevich Yu. (1986) Vetschestvennye chisla i ÉVM. In: V.A.Mel’nikov (ed.) Kibernetika i Vychislitel’naya technika 2, Nauka, Moscow, 104–133Google Scholar
  10. Moore R. E. (1966) Interval Analysis. Prentice Hall, Englewood CliffsMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Yuri Matiyasevich
    • 1
  1. 1.Saint-Petersburg Branch (POMI RAN)Steklov Institute of Mathematics of Russian Academy of SciencesSaint-PetersburgRussia

Personalised recommendations