Extending the range of error estimates for radial approximation in Euclidean space and on spheres

Details Extending the range of error estimates for radial approximation in Euclidean space and on spheres Extending the range of error estimates for radial approximation in Euclidean space and on spheres

2007-05-30

arxiv.org/abs/0705.4368v1

SIAM J. Math. Anal., 39(2):554-564, 2007

Mathematics

Numerical Analysis

10 pages

Scientific paper

10.1137/060650428

We adapt Schaback's error doubling trick [R. Schaback. Improved error bounds for scattered data interpolation by radial basis functions. Math. Comp., 68(225):201--216, 1999.] to give error estimates for radial interpolation of functions with smoothness lying (in some sense) between that of the usual native space and the subspace with double the smoothness. We do this for both bounded subsets of R^d and spheres. As a step on the way to our ultimate goal we also show convergence of pseudoderivatives of the interpolation error.

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