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›› 2009, Vol. 26 ›› Issue (2): 224-229.DOI: 10.7523/j.issn.2095-6134.2009.2.011

• Research Articles • Previous Articles     Next Articles

A block Gram-Schmidt algorithm with its application

ZHAO Tao1,2, JIANG Jin-Rong1   

  1. 1. Computer Network Information Center, Chinese Academy of Sciences, Beijing 100190, China;
    2. Graduate University, Chinese Academy of Sciences, Beijing 100049, China
  • Received:2008-04-30 Revised:2008-07-02 Online:2009-03-15

Abstract:

Gram-Schmidt algorithm is one of the fundamental methods in linear algebra, which is mainly used to compute QR decomposition. The classical and modified Gram-Schmidt are both based on level 1 or level 2 BLAS operations which have low cache reuse. In this paper, a new block Gram-Schmidt algorithm is proposed. The new algorithm ensures the orthogonality of resulting matrix Q is close to machine precision and improves performance because of using level 3 BLAS. Numerical experiments confirm the favorable numerical stability of the new algorithm and its effectiveness on modern computers.

Key words: Gram-Schmidt, Arnoldi algorithm, orthogonalization, block algorithm, QR

CLC Number: