Error estimation of floating-point summation and dot product

Publikationstyp
Journal Article
Date Issued
2011-06-10
Sprache
English
Author(s)
Rump, Siegfried M.  orcid-logo
Institut
Zuverlässiges Rechnen E-19  
TORE-URI
http://hdl.handle.net/11420/7915
Journal
BIT  
Volume
52
Issue
1
Start Page
201
End Page
220
Citation
BIT Numerical Mathematics 1 (52): 201-220 (2012-03-01)
Publisher DOI
10.1007/s10543-011-0342-4
Scopus ID
2-s2.0-84857690530
Publisher
Springer Science + Business Media B.V
We improve the well-known Wilkinson-type estimates for the error of standard floating-point recursive summation and dot product by up to a factor 2. The bounds are valid when computed in rounding to nearest, no higher order terms are necessary, and they are best possible. For summation there is no restriction on the number of summands. The proofs are short by using a new tool for the estimation of errors in floating-point computations which cures drawbacks of the "unit in the last place (ulp)". The presented estimates are nice and simple, and closer to what one may expect. © 2011 Springer Science + Business Media B.V.
Subjects
Dot product
Error analysis
Error bounds
Floating-point summation
Rounding
Unit in the first place (ufp)
Unit in the last place (ulp)
DDC Class
004: Informatik
510: Mathematik