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

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...

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Bibliographic Details
Published in:Numerical algorithms 2015-11, Vol.70 (3), p.653-667
Main Authors: Graillat, Stef, Lefèvre, Vincent, Muller, Jean-Michel
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Computation
Computer Science
Errors
Floating point arithmetic
Numeric Computing
Numerical Analysis
Original Paper
Other
Theory of Computation
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Description
Summary: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.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-015-9967-8