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Stability results for scattered-data interpolation on Euclidean spheres. (English) Zbl 0907.65006
Let $S^m$ be the unit sphere in $\bbfR^{m+1}$. A spherical-basis function approximant is a linear combination of the values of a given mapping $\varphi :[0, \pi ] \longrightarrow\bbfR$, 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 $S^1$.

65D05Interpolation (numerical methods)
41A05Interpolation (approximations and expansions)
41A30Approximation by other special function classes
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