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Direct and inverse Sobolev error estimates for scattered data interpolation via spherical basis functions. (English) Zbl 05200404
Summary: The purpose of this paper is to get error estimates for spherical basis function (SBF) interpolation and approximation for target functions in Sobolev spaces less smooth than the SBFs, and to show that the rates achieved are, in a sense, best possible. In addition, we establish a Bernstein-type theorem, where the smallest separation between data sites plays the role of a Nyquist frequency. We then use these Berstein-type estimates to derive inverse estimates for interpolation via SBFs.
MSC:
41A25Rate of convergence, degree of approximation
41A05Interpolation (approximations and expansions)
41A63Multidimensional approximation problems