摘要
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．这种方法从根本上避免了复数运算．此外，将重起动技术引入后，使算法具有迭代特点，不仅对计算重根非常有效，而且提供了判断是否漏根的机制，从而使该方法成为大型陀螺特征值问题完善的实用计算方法．算例表明了方法的有效性．
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.
出处
《固体力学学报》
CAS
CSCD
北大核心
1996年第4期283-289,共7页
Chinese Journal of Solid Mechanics
基金
国家自然科学基金
国家教委博士点基金
关键词
大型
陀螺特征值
反对称
减缩算法
large scale gyroscopic eigenvalue problem, skew symmetricity, Arnoldi reduction algorithm, restart technique
