%0 Journal Article
%T A block Gram-Schmidt algorithm with its application<br>分块Gram-Schmidt正交化算法及其应用
%A ZHAO Tao
%A JIANG Jin-Rong
%A <br>赵韬
%A 姜金荣
%J 中国科学院研究生院学报
%D 2009
%I 
%X 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.
%K Gram-Schmidt<br>Arnoldi算法
%K 正交化
%K 分块算法
%K QR分解
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=B5EDD921F3D863E289B22F36E70174A7007B5F5E43D63598017D41BB67247657&cid=B47B31F6349F979B&jid=67CDFDECD959936E166E0F72DE972847&aid=FA69C6FF5D06C984913933F0578FC11F&yid=DE12191FBD62783C&vid=96C778EE049EE47D&iid=0B39A22176CE99FB&sid=A1266CF37D675CF1&eid=F8035C8B7D8A4264&journal_id=1002-1175&journal_name=中国科学院研究生院学报&referenced_num=0&reference_num=15