Stability analysis and improvement of the block Gram-Schmidt algorithm

William Jalby 1 Bernard Philippe 1
1 CALCPAR - Calculateurs Parallèles
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, INRIA Rennes
Abstract : The advent of supercomputers with hierarchical memory systems has imposed the use of block algorithms for the linear algebra algorithms. Although block algorithms may result in impressive improvements in performance, their numerical properties are quite different from their scalar counterpart and deserve an in depth study. In this paper, the numerical stability of Block Gram Schmidt orthogonalization is studied and a variant is proposed which has numerical properties similar to the classical Modified-Gram-Schmidt while retaining most of the performance advantages of the block formulation.
Type de document :
Rapport
[Research Report] RR-1162, INRIA. 1990
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https://hal.inria.fr/inria-00075396
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Soumis le : mercredi 24 mai 2006 - 18:08:13
Dernière modification le : jeudi 11 janvier 2018 - 06:21:20
Document(s) archivé(s) le : mardi 12 avril 2011 - 22:55:24

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William Jalby, Bernard Philippe. Stability analysis and improvement of the block Gram-Schmidt algorithm. [Research Report] RR-1162, INRIA. 1990. 〈inria-00075396〉

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