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Reports (Research Report) Year : 2014

On the maximum relative error when computing $x^n$ in floating-point arithmetic

Vincent Lefèvre
Jean-Michel Muller

Abstract

In this paper, 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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Dates and versions

ensl-00945033 , version 1 (11-02-2014)
ensl-00945033 , version 2 (17-10-2014)

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Stef Graillat, Vincent Lefèvre, Jean-Michel Muller. On the maximum relative error when computing $x^n$ in floating-point arithmetic. [Research Report] Université Pierre et Marie Curie Paris 6; CNRS; Inria. 2014, pp.16. ⟨ensl-00945033v1⟩
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