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