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Scattered data interpolation on spheres: error estimates and locally supported basis functions. (English) Zbl 1055.41007
The paper works with the $n$-sphere as the underlying manifold for interpolation problem. There are obtained Sobolev-type error estimates for interpolating function $f\in C^{(2k)}(S^n)$ from ”shifts” by using of a smoother positive definite function $\phi$ on $S^n$. It is shown that the estimates are close to the optimal ones in order. It is also studied the class of locally supported positive definite functions on $S^n$, further functions based on Wendland’s compactly supported radia basis functions.

41A25Rate of convergence, degree of approximation
41A05Interpolation (approximations and expansions)
41A63Multidimensional approximation problems
42C10Fourier series in special orthogonal functions
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