BIT Numerical Mathematics

, Volume 16, Issue 2, pp 146-160

First online:

Taylor expansion of the accumulated rounding error

  • Seppo LinnainmaaAffiliated withDepartment of Computer Science, University of Helsinki

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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.