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Iterative methods for interval inclusion of fixed points

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Abstract

The paper discusses a technique for handling numerical, iterative processes that combines the efficiency of ordinary floating-point iterations with the accuracy control that may be obtained by iterations in interval arithmetic. As illustration the technique is used for the solution of fixed point problems in one and several variables.

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References

  1. R. E. Moore,Introduction to algebraic problems, InTopics in Interval Analysis (ed. E. Hansen), Oxford, (1969), 3–10.

  2. J. H. Wilkinson,Modern error analysis, SIAM Rev. 13 (1971), 548–568.

    Article  Google Scholar 

  3. Karl Nickel,Triplex-Algol and its applications, InTopics in Interval Analysis (ed. E. Hansen), Oxford, (1969), 10–25.

  4. Karl Nickel,Verbandstheoretische Grundlagen der Interval-Mathematik, InInterval Mathematics (ed. K. Nickel), Springer (1975), 251–263.

  5. G. Birkhoff,Lattice theory, Providence 1967 AMS.

  6. R. E. Moore,Interval analysis, Prentice-Hall, 1966.

  7. L. V. Kantorovich and G. P. Akilov,Functional analysis in normed spaces, Pergamon Press, 1964.

  8. F. N. Ris,Tools for the analysis of interval arithmetic, InInterval Mathematics (ed. K. Nickel), Springer (1975), 75–99.

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Authors and Affiliations

  1. Datalogisk Institut, Sigurdsgade 41, DK-2200, København N, Denmark

    Ole Caprani & Kaj Madsen

  2. Numerisk Institut Danmarks Tekniske Højskole, DK-2800, Lyngby, Denmark

    Ole Caprani & Kaj Madsen

Authors
  1. Ole Caprani
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  2. Kaj Madsen
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Caprani, O., Madsen, K. Iterative methods for interval inclusion of fixed points. BIT 18, 42–51 (1978). https://doi.org/10.1007/BF01947742

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  • DOI: https://doi.org/10.1007/BF01947742

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