Moderately high-dimensional approximation problems can successfully be solved by combining univariate approximation processes using an intelligent combination technique. While this has so far predominantly been done with either polynomials or splines, we suggest to employ a multilevel kernel-based approximation scheme. In contrast to those schemes built upon polynomials and splines, this new method is capable of combining arbitrary low-dimensional domains instead of just intervals and arbitrarily distributed points in these low-dimensional domains. We introduce the method and analyse its convergence in the so-called isotropic and anisotropic cases.

中文翻译：

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稀疏网格上基于核的多级方法的高维近似

通过使用智能组合技术组合单变量逼近过程可以成功解决中等高维逼近问题。虽然到目前为止这主要是通过多项式或样条函数完成的，但我们建议采用基于多级内核的近似方案。与那些基于多项式和样条曲线的方案相比，这种新方法能够组合任意低维域，而不仅仅是这些低维域中的区间和任意分布的点。我们介绍该方法并分析其在各向同性和各向异性情况下的收敛性。