Arnoldi方法简述及其在流动稳定性中的应用

流动稳定性问题常常归结于巨型非对称矩阵特征值问题。多数求解巨型非对称矩阵特征问题的算法均是经基本的Arnoldi算法演化而来。首先简述基本的Arnoldi算法; 其次简述基于Arnoldi算法的几类变体, 如显式重启Arnoldi算法，隐式重启Arnoldi算法与多重隐式重启Arnoldi算法; 最后基于Arnoldi算法及其变体结合谱位移技术求解计算流动稳定性问题, 并通过数值实验比较可知结合谱位移技术的多重隐式重启Arnoldi算法的求解效率最高。 

Arnoldi Method and Its Application in Flow Stability Problem

The problem of flow stability is often attributed to the eigenvalue problem of giant asymmetric matrix. Most algorithms for solving the eigenvalue problems of giant asymmetric matrices are evolved from the basic Arnoldi algorithm. Firstly, the basic Arnoldi algorithm was briefly described. Secondly, several variants based on Arnoldi algorithm were briefly described, such as explicitly restarted Arnoldi algorithm, implicitly restarted Arnoldi algorithm and multiple implicitly restarted Arnoldi algorithm. Finally, the Arnoldi algorithm and its variants, combined with spectral displacement technology to solve the problem of flow stability. Through numerical experiments, it is found that the multiple implicitly restarted Arnoldi algorithm combined with spectral displacement technology has the highest efficiency.