隐式重新启动的Lanczos算法在模型降阶中的应用

Implicitly Restarted Lanczos Algorithm for Model Reduction

主要研究了一种隐式重新启动的L anczos算法在模型降阶中的应用.分析了由这个算法得到的降价后的模型的一些性质,对于一个n阶稳定的线性时不变系统,模型降阶的思想是寻找一个m阶转换函数来近似原系统的n阶转换函数H(s),其中n m.传统的kry lov子空间方法仅仅产生一个不稳定的实现,并且在低频处的误差较大,本文所考虑的隐式重新启动的L anczos方法,能较好的解决上述两个问题.

This Paper considers an implicitly Lanczos Algorithm that approximates a stable, linear transfer function f（s） of order n by one of order m, where n〉〉m, It is well known that obilqtie projections onto a Krylov subspace may generate unstable partial realizations. A second difficulty arises from the fact that Krylov subspace methods often generate partial realizations that contain nonessential modes. The method considered in this paper can remedy these situation.