# 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} }

- Published 2008
DOI:10.1090/s0002-9947-2010-05070-6

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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#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 29 REFERENCES

## Scattered Data Approximation

VIEW 1 EXCERPT

## Approximation in L p ( R d ) from spaces spanned by the perturbed integer translates of a radial function

## A Bound on the Approximation Order of Surface Splines

VIEW 1 EXCERPT

## On the approximation order of principal shift-invariant subspaces of Lp(R)

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