ABSTRACT We investigate the time domain model order reduction (MOR) framework using general orthogonal polynomials by Jiang and Chen [1] 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.

中文翻译：

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LTI系统时域模型降阶与矩匹配的联系

摘要我们使用Jiang 和Chen [1] 的一般正交多项式研究了时域模型降阶（MOR）框架，并通过利用相应线性方程组的结构扩展了他们的想法。识别等效的 Sylvester 方程，我们展示了与有理 Krylov 子空间的联系，从而展示了与矩匹配的联系。三个数值示例说明了 MOR 技术之间的这种理论联系。对于线性时不变系统，该链接还激发了时域方法最多可以像矩匹配一样准确，因为扩展点通过多项式基的选择固定，而在矩匹配中它们可以适应系统。