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dc.contributor.author王元媛
dc.contributor.author卢琳璋
dc.date.accessioned2017-11-14T02:51:05Z
dc.date.available2017-11-14T02:51:05Z
dc.date.issued2008-09-15
dc.identifier.citation数学研究,2008,(03):22-32
dc.identifier.issn1006-6837
dc.identifier.otherSSYJ200803005
dc.identifier.urihttps://dspace.xmu.edu.cn/handle/2288/154818
dc.description.abstract在求块Toeplitz矩阵束(A_(mn),B_(mn))特征值的Lanczos过程中,通过对移位块Toepltz矩阵A_(mn)-ρB_(mn)进行基于sine变换的块预处理,从而改进了位移块Toeplitz矩阵的谱分布,加速了Lanczos过程的收敛速度.该块预处理方法能通过快速算法有效快速执行.本文证明了预处理后Lanczos过程收敛迅速,并通过实验证明该算法求解大规模矩阵问题尤其有效.
dc.description.abstractWe employ the block sine transform-based preconditioner to precondition the shifted block Toeplitz matrix A_(mn)-ρB_(mn) involved in the Lanczes method to compute the minimum eigenvalue of the generalized block Toeplitz eigenvalue problem A_(mn)x =λB_(mn)x,where A_(mn) and B_(mn) are partitioned into m×m blocks with order n.The block sine transform-based preconditioner can improve the spectral distribution of the shifted block Toeplitz matrix and,hence,can speed up the convergence rate of the preconditioned Lanczos method. The block sine transform-based preconditioner can be implemented efficiently by the fast transform algorithm. A convergence analysis shows that the preconditioned Lanczos method converges sufficiently fast,and numerical results show that this method is highly effective for large matrix.
dc.description.sponsorshipsupported by National Natural Science Foundation of China Nos 10531080
dc.language.isozh_CN
dc.subject分块Toeplitz矩阵
dc.subject双对称
dc.subjectsine变换
dc.subject预处理Lanczos方法
dc.subjectblock Toeplitz matrix
dc.subjectquadrantally symmetric
dc.subjectsine transform
dc.subjectpreconditioned Lanczos method
dc.title广义块Toeplitz特征值问题的基于sine变换的预处理子(英文)
dc.title.alternativeBlock Sine Transform Preconditioner for Generalized Block Toeplitz Eigenvalue Problem
dc.typeArticle


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