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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.
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Submitted on : Wednesday, May 24, 2006 - 6:08:13 PM
Last modification on : Friday, February 4, 2022 - 3:18:45 AM
Long-term archiving on: : Tuesday, April 12, 2011 - 10:55:24 PM


  • HAL Id : inria-00075396, version 1


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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