论文标题
在放松的过滤的Krylov子空间方法上，用于非对称特征值问题
On Relaxed Filtered Krylov Subspace Method for Non-Symmetric Eigenvalue Problems
论文作者
论文摘要
在本文中，通过引入一类放松的过滤的Krylov子空间，我们提出了放松的过滤后的Krylov子空间方法，用于计算具有最大真实零件的特征值和非对称矩阵的相应特征向量。作为副产品，还提出了过滤后的Krylov子空间法和用于求解非对称特征值问题的Chebyshev-Davidson方法的概括。我们对复杂的Chebyshev多项式进行了收敛分析，该分析在多项式加速技术中起着重要作用。此外，进行数值实验，以显示放松的过滤的Krylov子空间方法的鲁棒性及其优于某些最新技术迭代方法。
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.
