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

Katsuhisa Ozaki

doi:10.1063/1.4965377

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

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English
Title of host publication	Numerical Computations
Subtitle of host publication	Theory and Algorithms, NUMTA 2016: Proceedings of the 2nd International Conference "Numerical Computations: Theory and Algorithms"
Editors	Yaroslav D. Sergeyev, Marat S. Mukhametzhanov, Francesco Dell'Accio, Marat S. Mukhametzhanov, Dmitri E. Kvasov, Yaroslav D. Sergeyev, Dmitri E. Kvasov
Publisher	American Institute of Physics Inc.
ISBN (Electronic)	9780735414389
DOIs	https://doi.org/10.1063/1.4965377
Publication status	Published - 2016 Oct 20
Event	2nd International Conference on Numerical Computations: Theory and Algorithms, NUMTA 2016 - Pizzo Calabro, Italy Duration: 2016 Jun 19 → 2016 Jun 25

Publication series

Name	AIP Conference Proceedings
Volume	1776
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Other

Other	2nd International Conference on Numerical Computations: Theory and Algorithms, NUMTA 2016
Country	Italy
City	Pizzo Calabro
Period	16/6/19 → 16/6/25

ASJC Scopus subject areas

Physics and Astronomy(all)

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10.1063/1.4965377

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Ozaki, K. (2016). Improvement of the error bound for the dot product using the unit in the first place. In Y. D. Sergeyev, M. S. Mukhametzhanov, F. Dell'Accio, M. S. Mukhametzhanov, D. E. Kvasov, Y. D. Sergeyev, & D. E. Kvasov (Eds.), Numerical Computations: Theory and Algorithms, NUMTA 2016: Proceedings of the 2nd International Conference "Numerical Computations: Theory and Algorithms" [090013] (AIP Conference Proceedings; Vol. 1776). American Institute of Physics Inc.. https://doi.org/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". ed. / Yaroslav D. Sergeyev; Marat S. Mukhametzhanov; Francesco Dell'Accio; Marat S. Mukhametzhanov; Dmitri E. Kvasov; Yaroslav D. Sergeyev; Dmitri E. Kvasov. American Institute of Physics Inc., 2016. 090013 (AIP Conference Proceedings; Vol. 1776).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Ozaki, K 2016, Improvement of the error bound for the dot product using the unit in the first place. in YD Sergeyev, MS Mukhametzhanov, F Dell'Accio, MS Mukhametzhanov, DE Kvasov, YD Sergeyev & DE Kvasov (eds), Numerical Computations: Theory and Algorithms, NUMTA 2016: Proceedings of the 2nd International Conference "Numerical Computations: Theory and Algorithms"., 090013, AIP Conference Proceedings, vol. 1776, American Institute of Physics Inc., 2nd International Conference on Numerical Computations: Theory and Algorithms, NUMTA 2016, Pizzo Calabro, Italy, 16/6/19. https://doi.org/10.1063/1.4965377

Ozaki K. Improvement of the error bound for the dot product using the unit in the first place. In Sergeyev YD, Mukhametzhanov MS, Dell'Accio F, Mukhametzhanov MS, Kvasov DE, Sergeyev YD, Kvasov DE, editors, Numerical Computations: Theory and Algorithms, NUMTA 2016: Proceedings of the 2nd International Conference "Numerical Computations: Theory and Algorithms". American Institute of Physics Inc. 2016. 090013. (AIP Conference Proceedings). https://doi.org/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". editor / Yaroslav D. Sergeyev ; Marat S. Mukhametzhanov ; Francesco Dell'Accio ; Marat S. Mukhametzhanov ; Dmitri E. Kvasov ; Yaroslav D. Sergeyev ; Dmitri E. Kvasov. American Institute of Physics Inc., 2016. (AIP Conference Proceedings).

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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.",

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

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