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Tools for Mathematical Computation

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Computer Aided Proofs in Analysis

Part of the book series: The IMA Volumes in Mathematics and Its Applications ((IMA,volume 28))

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Abstract

Methodology for the validation of computation of values of functions using floatingpoint arithmetic is discussed and illustrated by an example.

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References

  1. G. Alefeld and J. Herzberger, Introduction to Interval Computations, Academic Press, 1983.

    MATH  Google Scholar 

  2. G. Bohlender, C. Ullrich, J. Wolff von Gudenberg, and L. B. Rall, Pascal-SC: A Computer Language for Scientific Computation, Academic Press, 1987.

    MATH  Google Scholar 

  3. George F. Corliss and L. B. Rall, Adaptive, self-validating numerical quadrature, SIAM J. Scientific and Statistical Computing, 8 (1987), 831–847 ().

    Article  MathSciNet  MATH  Google Scholar 

  4. U. Kulisch (Ed.), Pascal-SC for the IBM PC, B. G. Teubner, 1987.

    Google Scholar 

  5. U. Kulisch (Ed.), Pascal-SC for the Atari ST, B. G. Teubner, 1987.

    Google Scholar 

  6. U. W. Kulisch and W. L. Miranker, Computer Arithmetic in Theory and Practice, Academic Press, 1981.

    MATH  Google Scholar 

  7. U. W. Kulisch and W. L. Miranker (Eds.), A New Approach to Scientific Computation, Academic Press, 1983.

    MATH  Google Scholar 

  8. U. W. Kulisch and W. L. Miranker, The arithmetic of the digital computer: A new approach, SIAM Review, 28, (1986), 1–40.

    Article  MathSciNet  MATH  Google Scholar 

  9. R. E. Moore, Interval Analysis, Prentice-Hall, 1966.

    MATH  Google Scholar 

  10. R. E. Moore, Methods and Applications of Interval Analysis, Society for Industrial and Applied Mathematics, 1979.

    MATH  Google Scholar 

  11. R. E. Moore (Ed.), Reliability in Computing, Academic Press, 1988.

    MATH  Google Scholar 

  12. L. B. Rall, Computational Solution of Nonlinear Operator Equations, Wiley, 1969.

    MATH  Google Scholar 

  13. L. B. Rall, Automatic Differentiation: Techniques and Applications, Lecture Notes in Computer Science No. 120, Springer, 1981.

    MATH  Google Scholar 

  14. L. B. Rall, Mean value and Taylor forms in interval analysis, SIAM J. Math. Anal., 14 (1983) 223–238.

    Article  MathSciNet  MATH  Google Scholar 

  15. L. B. Rall, The arithmetic of differentiation, Math. Mag., 59, (1986), 275–282.

    Article  MathSciNet  MATH  Google Scholar 

  16. L. B. Rall, Pascal and Pascal-SC, in Encyclopedia of Physical Science and Technology, Vol. 10, pp. 183–209, Academic Press, 1987.

    Google Scholar 

  17. S. M. Rump, Solution of linear and nonlinear algebraic problems with sharp, guaranteed bounds, Computing, Suppl. 5 (1984), 147–168.

    Google Scholar 

  18. H. J. Stetter, Intervals revisited, Herrn Professor Dr. Karl Nickel zum 60. Geburtstag gewidmet, Vol. 2, pp. 519–538, University of Freiburg i. Br., 1984.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin, 53706, USA

    L. B. Rall

Authors
  1. L. B. Rall
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Editor information

Editors and Affiliations

  1. Departments of Mathematics and Computer Science, University of Cincinnati, Cincinnati, OH, 45221, USA

    Kenneth R. Meyer

  2. Department of Computer Science, University of Cincinnati, Cincinnati, OH, 45221, USA

    Dieter S. Schmidt

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© 1991 Springer-Verlag New York Inc.

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Rall, L.B. (1991). Tools for Mathematical Computation. In: Meyer, K.R., Schmidt, D.S. (eds) Computer Aided Proofs in Analysis. The IMA Volumes in Mathematics and Its Applications, vol 28. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9092-3_18

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  • DOI: https://doi.org/10.1007/978-1-4613-9092-3_18

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-9094-7

  • Online ISBN: 978-1-4613-9092-3

  • eBook Packages: Springer Book Archive

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