Radial basis interpolation on homogeneous manifolds: convergence rates |
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Authors: | J. Levesley D. L. Ragozin |
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Affiliation: | (1) Department of Mathematics, University of Leicester, Leicester, LE1 7RH, UK;(2) Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195, USA |
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Abstract: | Pointwise error estimates for approximation on compact homogeneous manifolds using radial kernels are presented. For a positive definite kernel κ the pointwise error at x for interpolation by translates of κ goes to 0 like ρ r , where ρ is the density of the interpolating set on a fixed neighbourhood of x. Tangent space techniques are used to lift the problem from the manifold to Euclidean space, where methods for proving such error estimates are well established. Partially supported by NSF Grant DMS-9972004. |
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Keywords: | scattered data interpolation homogeneous manifold radial basis functions zonal kernel convergence rates |
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