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Some Applications of Extended Interval Arithmetic to Interval Iterations

  • S. M. Markov
Part of the Computing Supplementum book series (COMPUTING, volume 2)

Abstract

The calculation of united extensions of real functions of one variable by means of primitive interval Operations is considered. It is demonstrated that extended interval arithmetic is a convenient tool for treating this problem. Some direct applications of the results obtained to interval iteration procedures are given.

Keywords

Real Function Interval Operator Contraction Mapping Banach Lattice Iteration Scheme 
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.

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References

  1. [1]
    Alefeld, G., Herzberger, J.: Einführung in die Intervallrechnung. Mannheim: Bibliographisches Institut 1974.zbMATHGoogle Scholar
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    Caprani, O., Madsen, K.: Contraction mappings in interval analysis. BIT 15, 362–366 (1975).CrossRefzbMATHGoogle Scholar
  3. [3]
    Markov, S.: Extended interval arithmetic. Compt. Rend. Acad. Bulg. Sei. 31, 163–166 (1978).zbMATHGoogle Scholar
  4. [4]
    Markov, S.: Extended interval arithmetic and some applications. Freiburger Intervall-Berichte 78/4, Institut für Angewandte Mathematik, Univ. Freiburg i. Br. 1978.Google Scholar
  5. [5]
    Moore, R. E.: Interval Analysis. Englewood Cliffs, N. J.: Prentice-Hall 1966.zbMATHGoogle Scholar
  6. [6]
    Nickel, K.: Intervall-Mathematik. ZAMM 58, T72-T85 (1978).zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • S. M. Markov
    • 1
  1. 1.Mathematisches InstitutBulgarische Akademie der WissenschaftenSofiaBulgaria

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