Publisher DOI: 10.1007/s10543-015-0555-z
Title: Improved error bounds for floating-point products and Horner’s scheme
Language: English
Authors: Rump, Siegfried M. 
Bünger, Florian 
Jeannerod, Claude Pierre 
Keywords: Floating-point product;Horner scheme;IEEE 754 standard;Wilkinson type error estimates
Issue Date: 24-Mar-2015
Publisher: Springer Science + Business Media B.V
Source: BIT Numerical Mathematics 1 (56): 293-307 (2016-03-01)
Journal or Series Name: BIT 
Abstract (english): Let (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.
ISSN: 1572-9125
Institute: Zuverlässiges Rechnen E-19 
Type: (wissenschaftlicher) Artikel
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