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求解对称特征值问题的块Chebyshev-Davidson方法

A BLOCK CHEBYSHEV-DAVIDSON METHOD FOR SOLVING SYMMETRIC EIGENPROBLEMS
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摘要 块Davidson方法是求解大型对称矩阵特征值问题块Lanczos方法的预处理变形.为了加速块Davidson方法的收敛性,我们组合块Chebyshev迭代法和块Davidson方法,提出了求解大型对称矩阵若干极端特征值的块Chebyshev-Davidson方法,并将收缩技术应用到该方法中.数值结果表明,块Chebyshev-Davidson方法优于块Davidson方法和Chebyshev-Davidson方法. The block Davidson method is a preconditioned variant of the block Lanczos method for solving large symmetric eigenvalue problems. In order to accelerate the convergence of the block Davidson method, we combine the block Chebyshev iteration with the block Davidson method and present the block Chebyshev-Davidson method with deflation for computing the extreme eigenvalues of large sparse symmetric matrices. Numerical results show that the block Chebyshev-Davidson method is far superior to the block Davidson method and the Chebyshev-Davidson method.
作者 梁觊 戴华
机构地区 南京航空航天大学数学系
出处 《数值计算与计算机应用》 CSCD 北大核心 2011年第3期209-219,共11页 Journal on Numerical Methods and Computer Applications
基金 中国科学院科学与工程计算国家重点实验室自主研究课题"大规模特征值问题的高效算法 理论与实现" 江苏省自然科学基金项目(BK2009364)的资助
关键词 对称矩阵 特征值 特征向量 Chebyshev加速 块Davidson方法 块Chebyshev—Davidson方法 symmetric matrix eigenvalue eigenvector, Chebyshev acceleration blockDavidson method block Chebyshev-Davidson method
分类号 O241.6 [理学—计算数学]
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参考文献19

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数值计算与计算机应用
2011年 第3期

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