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.

LanguageEnglish
Title of host publicationNumerical Computations: Theory and Algorithms, NUMTA 2016: Proceedings of the 2nd International Conference "Numerical Computations: Theory and Algorithms"
PublisherAmerican Institute of Physics Inc.
Volume1776
ISBN (Electronic)9780735414389
DOIs
StatePublished - 2016 Oct 20
Event2nd International Conference on Numerical Computations: Theory and Algorithms, NUMTA 2016 - Pizzo Calabro, Italy
Duration: 2016 Jun 192016 Jun 25

Other

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

Fingerprint

products
floating

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Ozaki, K. (2016). Improvement of the error bound for the dot product using the unit in the first place. In Numerical Computations: Theory and Algorithms, NUMTA 2016: Proceedings of the 2nd International Conference "Numerical Computations: Theory and Algorithms" (Vol. 1776). [090013] American Institute of Physics Inc.. DOI: 10.1063/1.4965377

Improvement of the error bound for the dot product using the unit in the first place. / Ozaki, Katsuhisa.

Numerical Computations: Theory and Algorithms, NUMTA 2016: Proceedings of the 2nd International Conference "Numerical Computations: Theory and Algorithms". Vol. 1776 American Institute of Physics Inc., 2016. 090013.

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

Ozaki, K 2016, Improvement of the error bound for the dot product using the unit in the first place. in Numerical Computations: Theory and Algorithms, NUMTA 2016: Proceedings of the 2nd International Conference "Numerical Computations: Theory and Algorithms". vol. 1776, 090013, American Institute of Physics Inc., 2nd International Conference on Numerical Computations: Theory and Algorithms, NUMTA 2016, Pizzo Calabro, Italy, 16/6/19. DOI: 10.1063/1.4965377
Ozaki K. Improvement of the error bound for the dot product using the unit in the first place. In Numerical Computations: Theory and Algorithms, NUMTA 2016: Proceedings of the 2nd International Conference "Numerical Computations: Theory and Algorithms". Vol. 1776. American Institute of Physics Inc.2016. 090013. Available from, DOI: 10.1063/1.4965377
Ozaki, Katsuhisa. / Improvement of the error bound for the dot product using the unit in the first place. Numerical Computations: Theory and Algorithms, NUMTA 2016: Proceedings of the 2nd International Conference "Numerical Computations: Theory and Algorithms". Vol. 1776 American Institute of Physics Inc., 2016.
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