SIAM Journal on Scientific Computing, Volume 43, Issue 1, Page A84-A108, January 2021.
In this work, we investigate a model-order reduction scheme for polynomial systems. We begin with defining the generalized multivariate transfer functions for the system. Based on this, we aim at constructing a reduced-order system, interpolating the defined generalized transfer functions at a given set of interpolation points. Furthermore, we provide a method, inspired by the Loewner approach for linear and (quadratic-)bilinear systems, to determine a good-quality reduced-order system in an automatic way. We also discuss the computational issues related to the proposed method and a potential application of a CUR matrix approximation in order to further speed up simulation of the reduced-order systems. We test the efficiency of the proposed method via two benchmark examples.

中文翻译：

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基于插值的多项式系统模型降阶

SIAM科学计算杂志，第43卷，第1期，第A84-A108页，2021年1月。
在这项工作中，我们研究了多项式系统的模型阶约简方案。我们首先定义系统的广义多元传递函数。基于此，我们旨在构建一个降阶系统，在给定的一组插值点处插值定义的广义传递函数。此外，我们提供了一种受Loewner方法启发的线性和（二次）双线性系统的方法，可以自动确定高质量的降阶系统。我们还将讨论与所提出的方法有关的计算问题以及CUR矩阵逼近的潜在应用，以进一步加快降阶系统的仿真速度。我们通过两个基准示例测试了该方法的效率。