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On the maximum relative error when computing integer powers by iterated multiplications in floating-point arithmetic

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Abstract

We improve the usual relative error bound for the computation of x n through iterated multiplications by x in binary floating-point arithmetic. The obtained error bound is only slightly better than the usual one, but it is simpler. We also discuss the more general problem of computing the product of n terms.

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Authors and Affiliations

  1. Sorbonne Universités, UPMC Univ Paris 06, UMR 7606, LIP6, F-75005, Paris, France

    Stef Graillat

  2. CNRS, UMR 7606, LIP6, F-75005, Paris, France

    Stef Graillat

  3. Inria, Laboratoire LIP, Université de Lyon, Lyon, France

    Vincent Lefèvre

  4. CNRS, Laboratoire LIP, Université de Lyon, Lyon, France

    Jean-Michel Muller

Authors
  1. Stef Graillat
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  2. Vincent Lefèvre
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  3. Jean-Michel Muller
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Correspondence to Stef Graillat.

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Graillat, S., Lefèvre, V. & Muller, JM. On the maximum relative error when computing integer powers by iterated multiplications in floating-point arithmetic. Numer Algor 70, 653–667 (2015). https://doi.org/10.1007/s11075-015-9967-8

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  • DOI: https://doi.org/10.1007/s11075-015-9967-8

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