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Improved error bounds for floating-point products and Horner’s scheme
Publikationstyp
Journal Article
Date Issued
2015-03-24
Sprache
English
Institut
TORE-URI
Journal
Volume
56
Issue
1
Start Page
293
End Page
307
Citation
BIT Numerical Mathematics 1 (56): 293-307 (2016-03-01)
Publisher DOI
Scopus ID
Publisher
Springer Science + Business Media B.V
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.
Subjects
Floating-point product
Horner scheme
IEEE 754 standard
Wilkinson type error estimates
DDC Class
004: Informatik