Extending the range of error estimates for radial approximation in Euclidean space and on spheres
SIAM journal on mathematical analysis, 2007•SIAM
We adapt Schaback's error doubling trick R. Schaback, Math. Comp., 68 (1999), pp. 201–
216 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.
216 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.
We adapt Schaback's error doubling trick [R. Schaback, Math. Comp., 68 (1999), pp. 201–216] 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 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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