Rump, Siegfried M.Siegfried M.RumpBünger, FlorianFlorianBüngerJeannerod, Claude PierreClaude PierreJeannerod2020-03-262020-03-262015-03-24BIT Numerical Mathematics 1 (56): 293-307 (2016-03-01)http://hdl.handle.net/11420/5500Let (Formula presented.) denote the relative rounding error of some floating-point format. Recently it has been shown that for a number of standard Wilkinson-type bounds the typical factors (Formula presented.) can be improved into (Formula presented.) , and that the bounds are valid without restriction on (Formula presented.). Problems include summation, dot products and thus matrix multiplication, residual bounds for (Formula presented.) - and Cholesky-decomposition, and triangular system solving by substitution. In this note we show a similar result for the product (Formula presented.) of real and/or floating-point numbers (Formula presented.) , for computation in any order, and for any base (Formula presented.). The derived error bounds are valid under a mandatory restriction of (Formula presented.). Moreover, we prove a similar bound for Horner’s polynomial evaluation scheme.en1572-912520151293307Springer Science + Business Media B.VFloating-point productHorner schemeIEEE 754 standardWilkinson type error estimatesInformatikJournal Article10.1007/s10543-015-0555-zOther