Improvement of the error bound for the dot product using the unit in the first place

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper is concerned with rounding error estimation for the dot product for numerical computations. Recently, Rump proposed a new type of error bounds for summation and the dot product using the unit in the first place of floating-point numbers. Our aim is to improve the error bound of the dot product. As a result, the constant of the error bound can be reduced.

Original languageEnglish
Title of host publicationNumerical Computations
Subtitle of host publicationTheory and Algorithms, NUMTA 2016: Proceedings of the 2nd International Conference "Numerical Computations: Theory and Algorithms"
EditorsYaroslav D. Sergeyev, Marat S. Mukhametzhanov, Francesco Dell'Accio, Marat S. Mukhametzhanov, Dmitri E. Kvasov, Yaroslav D. Sergeyev, Dmitri E. Kvasov
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735414389
DOIs
Publication statusPublished - 2016 Oct 20
Event2nd International Conference on Numerical Computations: Theory and Algorithms, NUMTA 2016 - Pizzo Calabro, Italy
Duration: 2016 Jun 192016 Jun 25

Publication series

NameAIP Conference Proceedings
Volume1776
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Other

Other2nd International Conference on Numerical Computations: Theory and Algorithms, NUMTA 2016
Country/TerritoryItaly
CityPizzo Calabro
Period16/6/1916/6/25

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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