中文摘要：

本文研究陀螺系统特征值问题的数值解法，利用反对称矩阵Lanczos算法，提出了求解陀螺系统特征值问题的二阶Lanczos方法．基于提出的陀螺系统特征值问题的非等价低秩收缩技术，给出了计算陀螺系统极端特征值的收缩二阶Lanczos方法．数值结果说明了算法的有效性．

英文摘要：

The numerical solutions for eigenvalue problems of gyroscopic systems are considered in this paper. By using Lanczos algorithm for skew-symmetric matrices, the second-order Lanczos method for solving eigenvalue problems of gyroscopic systems is presented. Based on the proposed non-equivalence low-rank deflation technique for eigenvalue problems of gyroscopic systems, a second-order Lanczos method with deflation for computing extreme eigenvalues of gyroscopic systems is given. The numerical results are included to demonstrate