大型陀螺特征值问题的广义Arnoldi减缩算法

基于Ａｒｎｏｌｄｉ法，建立陀螺特征值问题的广义Ａｒｎｏｌｄｉ格式，并利用系统矩阵的反对称特性，得到极其简洁的甚至比对称矩阵Ｌａｎｃｚｏｓ法更为简单的递推格式，可称为陀螺Ａｒｎｏｌｄｉ减缩算法。

ARNOLDI REDUCTION ALGORITHM FOR LARGE SCALE GYROSCOPIC EIGENVALUE PROBLEM

Based on Arnoldi's method, a version of the generalized Arnoldi algorithm was developed for the reduction of the gyroscopic eigenvalue problem. By utilizing the skew symmetricity of the system matrix, a very simple recurrence scheme, named gyroscopic Arnoldi reduction algorithm, was obtained. This algorithm is even simpler than the Lanczos alsorithm for the symmetric eigenvalue problem, and the complex number computation was completely avoided. In addition, the restart technique was employed to make the algorithm Possessing the iterative characteristics, it turned out that the resturt technique is not only efficient for calculating the multiple eigenvalues but also furnishes the reduction algorithm with a technique of checking and extracting the lossed eigenvalues. By combining with the resturt technique the algorithm was made practical for large scale gyroscopic eigenvalue problem. Numerical examples are given to demonstrate the effectiveness of the proposed method.