%0 Journal Article
%T A REFINED HARMONIC LANCZOS DIDIAGONALIZATION FOR COMPUTING SMALLEST SINGULAR TRIPLETS<br>计算最小奇异组的一个精化调和 Lanczos双对角化方法
%A Niu Datian
%A Jia Zhongxiao
%A Wang Kanmin
%A <br>牛大田
%A 贾仲孝
%A 王侃民
%J 计算数学
%D 2008
%I 
%X In many applications,one is required to compute several smallest singular triplets of large matrices.Harmonic projection methods are commonly used to compute interior eigenpairs of large matrices,and their principle can be applied to large singular value decomposition problems.It is proved that for sufficiently good subspaces the approximate singular values obtained by the harmonic projection methods converge while the corresponding approximate singular vectors may not.Based on the refined projection principle proposed by the second author,a refined harmonic Lanczos bidiagonalization method is proposed and its conver- gence is proved.In combination of the implicit restarting technique due to Sorensen,an implicitly restarted harmonic Lanczos bidiagonalzation algorithm (IRHLB) and its refined version (IRRHLB) are developed.A proper selection of shifts involved is one of the keys for the success of algorithms.A new shifts scheme,called refined harmonic shifts,is proposed for use within IRRHLB.Theoretical analysis shows that the refined shifts are better than the harmonic shifts used within IRHLB and they can be computed reliably and efficiently. Numerical experiments indicate that IRRHLB is considerably superior to IRHLB and better than the commonly used implicitly restarted Lanczos bidiagonalization algorithm (IRLB) and its refined version (IRRLB).
%K singular value
%K singular vector
%K the harmonic Lanczos bidiagonalization method
%K the refined harmonic Lanczos bidiagonalization method
%K approximate singular value
%K approximate singular vectors
%K implicit restarting
%K harmonic shifts
%K refined harmonic shifts
%K convergence<br>奇异值
%K 奇异向量
%K 调和Lanczos双对角化方法
%K 近似奇异值
%K 近似奇异向量
%K 精化调和Lanczos双对角化方法
%K 隐式重新启动
%K 调和位移
%K 精化调和位移
%K 收敛性
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=CC77F3CEF526D9CF0B3021650FB4E57E&aid=40898F28B139B3690266D0F31F3F66BC&yid=67289AFF6305E306&vid=340AC2BF8E7AB4FD&iid=38B194292C032A66&sid=A2745AA1110798CA&eid=377D325742940769&journal_id=0254-7791&journal_name=计算数学&referenced_num=0&reference_num=26