BIT Numerical Mathematics

, Volume 16, Issue 2, pp 146–160 | Cite as

Taylor expansion of the accumulated rounding error

  • Seppo Linnainmaa
Article

Abstract

The article describes analytic and algorithmic methods for determining the coefficients of the Taylor expansion of an accumulated rounding error with respect to the local rounding errors, and hence determining the influence of the local errors on the accumulated error. Second and higher order coefficients are also discussed, and some possible methods of reducing the extensive storage requirements are analyzed.

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References

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    P. Henrici,Elements of numerical analysis, Ch. 16, Wiley, New York, 1964.Google Scholar
  2. 2.
    S. Linnainmaa,The representation of the cumulative rounding error of an algorithm as a Taylor expansion of the local rounding errors, (In Finnish), Master's Thesis, Department of Computer Science, University of Helsinki, Helsinki, Finland, 1970.Google Scholar
  3. 3.
    S. Linnainmaa,Towards accurate statistical estimation of rounding errors in floating-point computations, BIT 15 (1975), 165–173.Google Scholar
  4. 4.
    S. Linnainmaa,A set of ALGOL procedures for analyzing the behavior of rounding errors in floating-point computations, Report A-1975-2, Department of Computer Science, University of Helsinki, Helsinki, Finland.Google Scholar
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    M. Tienari,A statistical model of roundoff errors for varying length floating-point arithmetic, BIT 10 (1970), 355–365.Google Scholar
  6. 6.
    M. Tienari,On some topological properties of numerical algorithms, BIT 12 (1972), 409–433.Google Scholar

Copyright information

© BIT Foundations 1976

Authors and Affiliations

  • Seppo Linnainmaa
    • 1
  1. 1.Department of Computer ScienceUniversity of HelsinkiHelsinki 10Finland

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