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Taylor expansion of the accumulated rounding error

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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Linnainmaa, S. Taylor expansion of the accumulated rounding error. BIT 16, 146–160 (1976). https://doi.org/10.1007/BF01931367

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Keywords

  • Computational Mathematic
  • Rounding Error
  • Taylor Expansion
  • Local Error
  • Storage Requirement