Error estimates for the summation of real numbers with application to floating-point summation

Marko Lange*, Siegfried M. Rump

*この研究の対応する著者

研究成果: Article査読

10 被引用数 (Scopus)

抄録

Standard Wilkinson-type error estimates of floating-point algorithms involve a factor γk: = ku/ (1 - ku) for u denoting the relative rounding error unit of a floating-point number system. Recently, it was shown that, for many standard algorithms such as matrix multiplication, LU- or Cholesky decomposition, γk can be replaced by ku, and the restriction on k can be removed. However, the arguments make heavy use of specific properties of both the underlying set of floating-point numbers and the corresponding arithmetic. In this paper, we derive error estimates for the summation of real numbers where each sum is afflicted with some perturbation. Recent results on floating-point summation follow as a corollary, in particular error estimates for rounding to nearest and for directed rounding. Our new estimates are sharp and unveil the necessary properties of floating-point schemes to allow for a priori estimates of summation with a factor omitting higher order terms.

本文言語English
ページ(範囲)927-941
ページ数15
ジャーナルBIT Numerical Mathematics
57
3
DOI
出版ステータスPublished - 2017 9月 1

ASJC Scopus subject areas

  • ソフトウェア
  • コンピュータ ネットワークおよび通信
  • 計算数学
  • 応用数学

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