中文摘要：

文章对带位移逆变换的隐式重启动Arnoldi（implicitly restarted Arnoldi，IRA）算法进行了改进，提出了动态增加Krylov 子空间维数求取指定圆内特征值的方法。论文从隐式重启动机理出发，在锁定已收敛特征值的基础上，动态增加特征值个数和子空间维数，扩大搜索圆的半径，实现指定大小的搜索圆内部所有特征值的有效求解。进而将电力系统关键特征值所在区域按一定规则分割，分割得到的所有小区域利用搜索圆覆盖求解。该方法不需人工干预，并行实现后效率更高，且搜索机制规避了漏解的现象。最后，状态空间为570阶和5272阶的电力系统的关键特征值计算结果表明，所提方法不仅高效，且可靠实用。

英文摘要：

On the basis of implicitly restarted Arnoldi （IRA） method, a method, in which the dimension of Krylov subspace is dynamically increased to compute eigenvalues in a specified circle, is proposed. In the implementation process of the proposed method, firstly, the radius of searching circles is dynamically expanded through increasing the number of eigenvalues and the dimension of Krylov subspace, according to the mechanism of implicitly restarting. Secondly, the region where the target eigenvalues located is divided into small computing units, which are covered by specified searching circles. The proposed method has higher efficiency after parallel implementation and avoids eigenvalues missing by searching mechanism compared with the existing methods. Furthermore, no manual intervention is needed in the proposed method. Two systems with 570 and 5 272 state variables are tested in this paper, and the results indicate that the proposed method is efficient, reliable and practical.