Summary.
Interpolation with translates of a basis function is a common process in approximation theory. The most elementary form of the interpolant consists of a linear combination of all translates by interpolation points of a single basis function. Frequently, low degree polynomials are added to the interpolant. One of the significant features of this type of interpolant is that it is often the solution of a variational problem. In this paper we concentrate on developing a wide variety of spaces for which a variational theory is available. For each of these spaces, we show that there is a natural choice of basis function. We also show how the theory leads to efficient ways of calculating the interpolant and to new error estimates.
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Received December 10, 1996 / Revised version received August 29, 1997
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Light, W., Wayne, H. Spaces of distributions, interpolation by translates of a basis function and error estimates. Numer. Math. 81, 415–450 (1999). https://doi.org/10.1007/s002110050398
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DOI: https://doi.org/10.1007/s002110050398