Variably scaled kernels and mapped bases constructed via the so-called fake nodes approach are two different strategies to provide adaptive bases for function interpolation. In this paper, we focus on kernel-based interpolation and we present what we call mapped variably scaled kernels, which take advantage of both strategies. We present some theoretical analysis and then we show their efficacy via numerical experiments. Moreover, we test such a new basis for image reconstruction tasks in the framework of hard X-ray astronomical imaging.

翻译：可变比例核和通过所谓的“假节点”方法构造的映射基是提供函数插值自适应基的两种不同策略。在本文中，我们聚焦于基于核的插值，并提出了我们所称的映射可变比例核，它们利用了这两种策略的优势。我们展示了一些理论分析，然后通过数值实验证明了其有效性。此外，我们在硬X射线天文成像框架下测试这种新基础以进行图像重建任务。