求解非对称特征值问题的过滤类Krylov序列方法

On the Filtered KrylovLike Sequence Method for Solving Non-Symmetric Eigenvalue Problems

将标准Krylov子空间方法及多项式加速技术整合起来的过滤类Krylov序列方法对求解对称矩阵的多个端部特征值极为高效.本文将该方法推广,以求解非对称矩阵的实部最大的特征值及其对应的特征向量.与标准Krylov子空间方法相比,过滤类Krylov序列方法具有极大的优越性和鲁棒性.数值实验表明了新方法的有效性.

The filtered Krylov­like sequence method,which integrates the standard Krylov subspace method with the polynomial filtering technique,is efficient for computing several extreme eigenvalues of symmetric matrices.In this paper,we generalize this method to compute the eigenvalues with largest real parts and the corresponding eigenvectors of non­-symmetric matrices.The filtered Krylov­-like sequence method can be expected to show great superiority and robustness over the standard Krylov subspace methods.Numerical experiments are carried out to show competitiveness of the new method.