时域模型降阶与线性时不变系统矩匹配之间的一种联系
A Connection Between Time Domain Model Order Reduction and Moment Matching for LTI Systems
AI总结：
本文研究了时域模型降阶方法与线性时不变系统矩匹配之间的联系，通过三个数值例子展示了理论联系，并指出时域方法的精度不高于矩匹配，因为展开点由多项式基的选择决定，而矩匹配可以适应系统。
摘要：
我们研究了Jiang和Chen 2012提出的时域模型降阶（MOR）框架，利用一般的正交多项式，并通过利用相应线性方程组的结构扩展了他们的想法。通过识别等价的Sylvester方程，我们展示了该MOR技术与有理Krylov子空间以及矩匹配之间的联系。这种理论联系通过三个数值例子加以说明。对于线性时不变系统，这种联系也表明时域方法的准确性至多与矩匹配相当，因为展开点由多项式基的选择决定，而矩匹配可以适应系统。
英文摘要：
We investigate the time domain model order reduction (MOR) framework using general orthogonal polynomials by Jiang and Chen 2012 and extend their idea by exploiting the structure of the corresponding linear system of equations. Identifying an equivalent Sylvester equation, we show a connection to a rational Krylov subspace, and thus to moment matching. This theoretical link between the MOR techniques is illustrated by three numerical examples. For linear time-invariant systems, the link also motivates that the time domain approach can be at best as accurate as moment matching, since the expansion points are fixed by the choice of the polynomial basis, while in moment matching they can be adapted to the system.
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