On relaxed filtered Krylov subspace method for non-symmetric eigenvalue problems
On relaxed filtered Krylov subspace method for non-symmetric eigenvalue problems
复制标题
非对称特征值问题的松弛滤波Krylov子空间方法
DOI：
10.1016/j.cam.2021.113698
复制
发表时间：
2021
影响因子：
2.4
通讯作者：
Wu Wen-Ting
中科院分区：
文献类型：
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作者：
Miao Cun-Qiang;Wu Wen-Ting
通过引入一类松弛滤子Krylov子空间，提出了计算非对称矩阵最大真实的部分特征值及相应特征向量的松弛滤子Krylov子空间方法.作为副产品，过滤Krylov子空间方法和Chebyshev-Davidson方法求解非对称特征值问题的推广。本文给出了复Chebyshev多项式的收敛性分析，它在多项式加速技术中起着重要的作用。此外，数值实验表明，松弛滤波Krylov子空间方法的鲁棒性和它的巨大优势，比一些国家的最先进的迭代方法。
In this paper, by introducing a class of relaxed filtered Krylov subspaces, we propose the relaxed filtered Krylov subspace method for computing the eigenvalues with the largest real parts and the corresponding eigenvectors of non-symmetric matrices. As by-products, the generalizations of the filtered Krylov subspace method and the Chebyshev–Davidson method for solving non-symmetric eigenvalue problems are also presented. We give the convergence analysis of the complex Chebyshev polynomial, which plays a significant role in the polynomial acceleration technique. In addition, numerical experiments are carried out to show the robustness of the relaxed filtered Krylov subspace method and its great superiority over some state-of-the-art iteration methods.