论文标题
插值$ \ MATHCAL {L} _2 $ - 最佳降低订购建模的统一框架
A Unifying Framework for Interpolatory $\mathcal{L}_2$-optimal Reduced-order Modeling
论文作者
论文摘要
我们为插值$ \ MATHCAL {L} _2 $ - 最佳的减少订单建模开发了一个统一的框架，从固定模型到参数动力学系统，针对各种各样的问题。我们首先表明该框架自然涵盖了$ \ Mathcal {h} _2 $ -Optimal模型订单减少的必要条件，并导致$ \ MATHCAL {H} _2 _2 _2 \ outimime \ otimes \ Mathcal {l} _2 $ -Optimal Models Models Multii Intuction/Multii caramuttim/yuntuctim rectuction/yuntim rectuction/yumbion caramition/yumert caramution/yumert rectuction/yuntuction/乘，此外，我们为合理离散最小二乘最小化的新型插值最佳条件以及$ \ Mathcal {l} _2 $ - 最佳模型订单降低一类参数固定模型的降低。我们表明，位于跨不同领域的最佳性的主要工具是Bitisgential Hermite插值。在两个数值示例中说明了理论结果。
We develop a unifying framework for interpolatory $\mathcal{L}_2$-optimal reduced-order modeling for a wide classes 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 $\mathcal{H}_2$-optimal model order reduction and leads to the interpolatory conditions for $\mathcal{H}_2 \otimes \mathcal{L}_2$-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 $\mathcal{L}_2$-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 on two numerical examples.
