Stability results for scattered-data interpolation on Euclidean spheres. (English) Zbl 0907.65006

Let \(S^m\) be the unit sphere in \(\mathbb{R}^{m+1}\). A spherical-basis function approximant is a linear combination of the values of a given mapping \(\varphi :[0, \pi ] \longrightarrow\mathbb{R}\), where the arguments are geodesic distances in \(S^m\). If \(\varphi\) is a strictly positive definite function in \(S^m\) then the interpolation matrix is positive definite for every choice of the points. The authors study a subclass of such functions \(\varphi\) and the stability estimates for the associated interpolation matrices are given. The last section contains the interpolation on the unit circle \(S^1\).


65D05 Numerical interpolation
41A05 Interpolation in approximation theory
41A30 Approximation by other special function classes
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