%0 Journal Article
%T THE MULTI-RITZ-VECTOR METHOD IN GENERALIZED EIGENVALUE PROBLEMS<br>求解广义特征值问题的多重Ritz向量法
%A Huang Jifeng
%A <br>黄吉锋
%J 力学学报
%D 1999
%I 
%X With reference to the subspace iteration method, the normal Ritz-Vector methodis extended to an improved one i.e. the Multi-Ritz-Vector method in this paper by which theproblem of eigen-value losing for the systems with multi-fold eigen--value in the normal Ritz--Vectormethod can be solved and no eigen-vectors corresponding to multi-fold eigen--value will be lost.Then, it has been pointed out that a singular or ill-conditioned matrix M would lead to anunstable M-orthogonalization procedure of Gram-Schmidt and then yield incorrect eigen-vectorsif the normal Ritz--Vector method was directly used to a system with singular mass matrix. In theMulti-Ritz-Vector method, am elaborate algorithm is proposed in order to improve the stability ofthe computational procedure of the normal Ritz-Vector method. By incorporation of the abovetwo modifications, an improved method i.e. the Multi-Ritz-Vector method which is much moreefficient and reliable than the normal one is obtained.
%K subspace iteration method
%K Lanczos method
%K Ritz-Vector method
%K multi-Ritz-Vectormethod
%K multi-fold eigenvalue<br>子空间迭代法
%K 多重Ritz向量法
%K 多重特征值
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=5D344E2AD54D14F8&jid=4100DA4A1A3BA1B0CE5AD99AE1DFB420&aid=2515060DC59C9C454581FC75A435D78A&yid=B914830F5B1D1078&vid=4AD960B5AD2D111A&iid=94C357A881DFC066&sid=E513158F1BE1471F&eid=240CB58995465C01&journal_id=0459-1879&journal_name=力学学报&referenced_num=0&reference_num=10