Approximation using scattered shifts of a multivariate function

@inproceedings{Devore2008ApproximationUS,
  title={Approximation using scattered shifts of a multivariate function},
  author={Ronald M. Devore and Amos Ron},
  year={2008}
}
The approximation of a general $d$-variate function $f$ by the shifts $\phi(\cdot-\xi)$, $\xi\in\Xi\subset \Rd$, of a fixed function $\phi$ occurs in many applications such as data fitting, neural networks, and learning theory. When $\Xi=h\Z^d$ is a dilate of the integer lattice, there is a rather complete understanding of the approximation problem \cite{BDR,Johnson1} using Fourier techniques. However, in most applications the {\it center} set $\Xi$ is either given, or can be chosen with… CONTINUE READING

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