Spaces of distributions, interpolation by translates of a basis function and error estimates |
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Authors: | Will Light Henry Wayne |
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Institution: | (1) Department of Mathematics and Computer Science, University of Leicester, University Road, Leicester, LE1 7HR, UK , GB |
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Abstract: | 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.
Received December 10, 1996 / Revised version received August 29, 1997 |
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Keywords: | Mathematics Subject Classification (1991):65D05 |
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