A New Distillation Algorithm for Floating-Point Summation

Jun-Hai Yong 1 Guo-Qin Zheng 1 Yong-Kang Zhu 1
1 CAD - Computer Aided Design
LIAMA - Laboratoire Franco-Chinois d'Informatique, d'Automatique et de Mathématiques Appliquées, Inria Paris-Rocquencourt
Abstract : The summation of n floating-point numbers is ubiquitous in numerical computations. We present a new distillation algorithm for floating-point summation which is stable, efficient, and accurate. The algorithm iteratively "distills" the summands without discarding any significant digit until the partial sums cannot change the whole sum. It uses standard floating-point arithmetic and does not rely on the choice of radix or any other specific assumption. Furthermore, the error bound of our algorithm is independent of n and less than 1 ulp.
Type de document :
Article dans une revue
SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2005, 26 (6), pp.2066-2078. 〈10.1137/030602009〉
Liste complète des métadonnées

https://hal.inria.fr/inria-00143168
Contributeur : Chine Publications Liama <>
Soumis le : mardi 24 avril 2007 - 15:16:54
Dernière modification le : jeudi 11 janvier 2018 - 06:21:19

Lien texte intégral

Identifiants

Collections

Citation

Jun-Hai Yong, Guo-Qin Zheng, Yong-Kang Zhu. A New Distillation Algorithm for Floating-Point Summation. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2005, 26 (6), pp.2066-2078. 〈10.1137/030602009〉. 〈inria-00143168〉

Partager

Métriques

Consultations de la notice

134