  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.
