Convergence Estimates for the Generalized Davidson Method for Symmetric Eigenvalue Problems II: The Subspace Acceleration
Convergence Estimates for the Generalized Davidson Method for Symmetric Eigenvalue Problems II: The Subspace Acceleration
复制标题
对称特征值问题的广义戴维森方法的收敛性估计 II：子空间加速
DOI：
10.1137/s0036142902411768
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
E. Ovtchinnikov
中科院分区：
文献类型：
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作者：
E. Ovtchinnikov
广义Davidson （GD）方法可以看作是求解对称特征值问题的预条件最陡下降（PSD）方法的推广。在GD方法中，除了PSD中使用的当前特征向量及其预条件残差外，还在跨所有先前近似特征向量的子空间中寻找新的近似。在这方面，GD和PSD方法之间的关系类似于线性系统的标准最陡下降法和Krylov子空间中的方法之间的关系。本文给出了（重启）GD方法的收敛估计，与PSD方法相比，它证明了收敛加速，类似于在Krylov子空间中与标准最陡下降相比的方法所实现的收敛速度。
The generalized Davidson (GD) method can be viewed as a generalization of the preconditioned steepest descent (PSD) method for solving symmetric eigenvalue problems. In the GD method, the new approximation is sought in the subspace that spans all the previous approximate eigenvectors, in addition to the current one and the preconditioned residual thereof used in PSD. In this respect, the relation between the GD and PSD methods is similar to that between the standard steepest descent method for linear systems and methods in Krylov subspaces. This paper presents convergence estimates for the (restarted) GD method that demonstrate convergence acceleration compared to the PSD method, similar to that achieved by methods in Krylov subspaces compared to the standard steepest descent.