Harmonic and refined harmonic shift-invert residual Arnoldi and Jacobi--Davidson methods for interior eigenvalue problems
Harmonic and refined harmonic shift-invert residual Arnoldi and Jacobi--Davidson methods for interior eigenvalue problems
复制标题
谐波和精化谐波移位-求逆残差Arnoldi和Jacobi--内特征值问题的戴维森方法
DOI：
10.1016/j.cam.2014.12.043
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发表时间：
2015
影响因子：
2.4
通讯作者：
Li Cen
中科院分区：
文献类型：
--
作者：
Jia Zhongxiao;Li Cen
This paper concerns the harmonic shift-invert residual Arnoldi (HSIRA) and Jacobi–Davidson (HJD) methods as well as their refined variants RHSIRA and RHJD for the interior eigenvalue problem. Each method needs to solve an inner linear system to expand the subspace successively. When the linear systems are solved only approximately, we are led to the inexact methods. We prove that the inexact HSIRA, RHSIRA, HJD and RHJD methods mimic their exact counterparts well when the inner linear systems are solved with onlylowormodestaccuracy. We show that (i) the exact HSIRA and HJD expand subspaces better than the exact SIRA and JD and (ii) the exact RHSIRA and RHJD expand subspaces better than the exact HSIRA and HJD. Based on the theory, we design stopping criteria for inner solves. To be practical, we present restarted HSIRA, HJD, RHSIRA and RHJD algorithms. Numerical results demonstrate that these algorithms are much more efficient than the restarted standard SIRA and JD algorithms and furthermore the refined harmonic algorithms outperform the harmonic ones very substantially.
