Kernel based approximation offers versatile tools for high-dimensional approximation, which can especially be leveraged for surrogate modeling. For this purpose, both "knot insertion" and "knot removal" approaches aim at choosing a suitable subset of the data, in order to obtain a sparse but nevertheless accurate kernel model. In the present work, focussing on kernel based interpolation, we aim at combining these two approaches to further improve the accuracy of kernel models, without increasing the computational complexity of the final kernel model. For this, we introduce a class of kernel exchange algorithms (KEA). The resulting KEA algorithm can be used for finetuning greedy kernel surrogate models, allowing for an reduction of the error up to 86.4% (17.2% on average) in our experiments.

翻译：基于核的逼近方法为高维逼近提供了多功能工具，尤其适用于代理建模。为此，"节点插入"和"节点移除"方法均致力于选择合适的数据子集，以获得稀疏但精确的核模型。在本文中，我们聚焦于基于核的插值，旨在结合这两种方法以进一步提高核模型的精度，同时不增加最终核模型的计算复杂度。为此，我们引入了一类核交换算法（KEA）。所提出的KEA算法可用于微调贪婪核代理模型，在我们的实验中，该算法可使误差降低高达86.4%（平均降低17.2%）。