A Unifying Framework for Interpolatory \({\boldsymbol{\mathcal{L}_2}}\)-Optimal Reduced-Order Modeling
A Unifying Framework for Interpolatory \({\boldsymbol{\mathcal{L}_2}}\)-Optimal Reduced-Order Modeling
复制标题
插值({oldsymbol{mathcal{L}_2}})-最优降阶建模的统一框架
DOI：
10.1137/22m1516920
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发表时间：
2023
影响因子：
2.9
通讯作者：
Gugercin, Serkan
中科院分区：
文献类型：
--
作者：
Mlinarić, Petar;Gugercin, Serkan
我们为从平稳模型到参数动力系统的广泛问题开发了一个统一的插值最优降阶建模框架。我们首先表明，该框架自然地涵盖了众所周知的最优模型降阶的插值必要条件，并导致了多输入/多输出参数动力系统的最优模型降阶的插值条件。此外，我们还导出了一类参数平稳模型的有理离散最小二乘最小化和最优模型降阶的插值最优性条件。我们表明，双向Hermite插值是跨不同域的最优性的主要工具。通过两个算例对理论结果进行了说明。
We develop a unifying framework for interpolatory-optimal reduced-order modeling for a wide class of problems ranging from stationary models to parametric dynamical systems. We first show that the framework naturally covers the well-known interpolatory necessary conditions for-optimal model order reduction and leads to the interpolatory conditions for-optimal model order reduction of multi-input/multi-output parametric dynamical systems. Moreover, we derive novel interpolatory optimality conditions for rational discrete least-squares minimization and for-optimal model order reduction of a class of parametric stationary models. We show that bitangential Hermite interpolation appears as the main tool for optimality across different domains. The theoretical results are illustrated in two numerical examples.