ABSTRACT In this contribution, a new framework for -optimal reduction is presented, motivated by the local nature of both (tangential) interpolation and -optimal approximations. The main advantage is given by a decoupling of the cost of reduction from the cost of optimization, resulting in a significant speedup in -optimal reduction. In addition, a middle-sized surrogate model is produced at no additional cost and can be used e.g. for error estimation. Numerical examples illustrate the new framework, showing its effectiveness in producing -optimal reduced models at a far lower cost than conventional algorithms. Detailed discussions and optimality proofs are presented for applying this framework to the reduction of multiple-input, multiple-output linear dynamical systems. The paper ends with a brief discussion on how this framework could be extended to other system classes, thus indicating how this truly is a general framework for interpolatory reduction.

中文翻译：

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H2-最优模型约简的新框架

摘要 在这个贡献中，提出了一个新的优化减少框架，其动机是（切向）插值和优化近似的局部性质。主要优势在于减少成本与优化成本的分离，从而显着加快了优化减少的速度。此外，无需额外成本即可生成中等规模的替代模型，并可用于例如误差估计。数值示例说明了新框架，显示了它在以远低于传统算法的成本生成最佳简化模型方面的有效性。详细的讨论和最优性证明被提出来应用这个框架来减少多输入、多输出线性动力系统。