BIT Numerical Mathematics

, Volume 16, Issue 2, pp 146–160

Taylor expansion of the accumulated rounding error


  • Seppo Linnainmaa
    • Department of Computer ScienceUniversity of Helsinki

DOI: 10.1007/BF01931367

Cite this article as:
Linnainmaa, S. BIT (1976) 16: 146. doi:10.1007/BF01931367


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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© BIT Foundations 1976