摘要
Gram-Schmidt正交化算法是数值线性代数中的基本算法之一,主要用于计算矩阵QR分解.经典和修正Gram-Schmidt正交化算法基于level1/2BLAS运算,低级BLAS运算对cache的利用率比较低,从而限制了算法性能.提出一种新的分块Gram-Schmidt正交化算法.新算法通过重正交保证产生矩阵Q的正交性达到机器精度,并且利用level3BLAS运算提高了算法性能.数值试验表明,新算法能使得矩阵Q的正交性达到机器精度,并且新算法使得性能得到显著提高.
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 modem computers.
出处
《中国科学院研究生院学报》
CAS
CSCD
北大核心
2009年第2期224-229,共6页
Journal of the Graduate School of the Chinese Academy of Sciences
基金
国家自然科学基金(60533020)
中国科学院知识创新工程青年人才领域项目(O714051A01)资助
