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Journal Articles Numerical Algorithms Year : 2015

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

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Vincent Lefèvre
Jean-Michel Muller

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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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 integer powers by iterated multiplications in floating-point arithmetic. Numerical Algorithms, 2015, 70 (3), pp.653-667. ⟨10.1007/s11075-015-9967-8⟩. ⟨ensl-00945033v2⟩
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