On the maximum relative error when computing integer powers by iterated multiplications in floating-point arithmetic
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We improve the usual relative error bound for the computation of xn 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.
KeywordsFloating-point arithmetic Rounding error Accurate error bound Exponentiation
Mathematics Subject Classification (2010)15-04 65G99 65-04
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