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.

在本文中，通过引入一类松弛滤波Krylov子空间，我们提出了松弛滤波Krylov子空间方法来计算具有最大实部的特征值和非对称矩阵的相应特征向量。作为副产品，还介绍了用于解决非对称特征值问题的滤波 Krylov 子空间方法和 Chebyshev-Davidson 方法的推广。我们给出了复切比雪夫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，还进行了数值实验，以展示松弛滤波 Krylov 子空间方法的鲁棒性及其相对于一些最先进的迭代方法的巨大优势。