Computer Engineering and Applications ›› 2016, Vol. 52 ›› Issue (12): 251-255.

Previous Articles     Next Articles

Arnoldi model reduction method based on implicitly restarted Krylov-Schur technology

XU Kangli1, YANG Zhixia1, JIANG Yaolin2   

  1. 1.College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China
    2.School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China
  • Online:2016-06-15 Published:2016-06-14

基于Krylov-Schur重启技术的Arnoldi模型降阶方法

徐康丽1,杨志霞1,蒋耀林2   

  1. 1.新疆大学 数学与系统科学学院,乌鲁木齐 830046
    2.西安交通大学 数学与统计学院,西安 710049

Abstract: Krylov subspace method is one of the typical model reduction methods, in which Arnoldi model reduction method is the basic method. Re-orthogonalizational Arnoldi algorithm is proposed to obtain r step Arnoldi decomposition. Next, this paper restarts Krylov-Schur process and drives Arnoldi model reduction method based on implicitly restarted Krylov-Schur technology to reduce the large scale linearly time invariant systems. By this method, it can obtain a stable order-reduced system with higher accuracy, which can improve the drawback of Krylov subspace methods. Finally, simulations of a linearly time invariant system will be conducted to illustrate the effectiveness of the proposed method.

Key words: model-order reduction, Krylov subspace methods, re-orthogonalization;implicitly restarted Krylov-Schur technology

摘要: Krylov子空间模型降阶方法是模型降阶中的典型方法之一,Arnoldi模型降阶方法是这类方法中的一类基本方法。运用重正交化的Arnoldi算法得到[r]步Arnoldi分解;执行Krylov-Schur重启过程,导出基于Krylov-Schur重启技术的Arnoldi模型降阶方法。运用此方法对大规模线性时不变系统进行降阶,得到具有较高近似精度的稳定的降阶系统,从而改善了Krylov子空间降阶方法不能保持降阶系统稳定性的不足。数值算例验证了此方法是行之有效的。

关键词: 模型降阶, Krylov子空间方法, 重正交化, Krylov-Schur重启技术