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

TL;DR

This paper refines the error bounds for computing x^n in floating-point arithmetic, providing a simpler yet slightly improved estimate, and discusses broader product computation issues.

Contribution

It offers a simplified, marginally tighter relative error bound for x^n calculations in floating-point arithmetic and explores general product computation problems.

Findings

Improved error bound is simpler than traditional bounds.

The new bound is only slightly better but easier to understand.

Discusses generalization to product of n terms.

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.