Abstract
Pointwise error estimates for approximation on compact homogeneous manifolds using radial kernels are presented. For a \({\mathcal C}^{2r}\) 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.
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Communicated by J. Levesley.
Supported by EPSRC Grant GR/L36222.
Partially supported by NSF Grant DMS-9972004.
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Levesley, J., Ragozin, D.L. Radial basis interpolation on homogeneous manifolds: convergence rates. Adv Comput Math 27, 237–246 (2007). https://doi.org/10.1007/s10444-005-9000-1
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DOI: https://doi.org/10.1007/s10444-005-9000-1