On the maximum relative error when computing x^n in floating-point arithmetic
Numerical Analysis
2014-02-14 v1 Numerical Analysis
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.
Cite
@article{arxiv.1402.2991,
title = {On the maximum relative error when computing x^n in floating-point arithmetic},
author = {Stef Graillat and Vincent Lefèvre and Jean-Michel Muller},
journal= {arXiv preprint arXiv:1402.2991},
year = {2014}
}