Accurate sum and dot product

Takeshi Ogita*, Siegfried M. Rump, Shin'ichi Oishi

*この研究の対応する著者

研究成果: Article査読

219 被引用数 (Scopus)

抄録

Algorithms for summation and dot product of floating-point numbers are presented which are fast in terms of measured computing time. We show that the computed results are as accurate as if computed in twice or AT-fold working precision, K ≥ 3. For twice the working precision our algorithms for summation and dot product are some 40% faster than the corresponding XBLAS routines while sharing similar error estimates. Our algorithms are widely applicable because they require only addition, subtraction, and multiplication of floating-point numbers in the same working precision as the given data. Higher precision is unnecessary, algorithms are straight loops without branch, and no access to mantissa or exponent is necessary.

本文言語English
ページ(範囲)1955-1988
ページ数34
ジャーナルSIAM Journal on Scientific Computing
26
6
DOI
出版ステータスPublished - 2005

ASJC Scopus subject areas

  • 計算数学
  • 応用数学

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