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：变尺度核函数与基于所谓虚拟节点方法构造的映射基是两种为函数插值提供自适应基函数的不同策略。本文聚焦于基于核函数的插值方法，提出了一种结合两种策略优势的映射变尺度核函数。我们进行了部分理论分析，并通过数值实验验证了其有效性。此外，我们将这种新型基函数应用于硬X射线天文成像领域的图像重建任务中进行了测试。