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.


41A25 Rate of convergence, degree of approximation
41A05 Interpolation in approximation theory
41A63 Multidimensional problems
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
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