Narcowich, F. J.; Sivakumar, N.; Ward, J. D. Stability results for scattered-data interpolation on Euclidean spheres. (English) Zbl 0907.65006 Adv. Comput. Math. 8, No. 3, 137-163 (1998). 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 \(S^1\). Reviewer: N.Ţăndăreanu (Craiova) Cited in 10 Documents MSC: 65D05 Numerical interpolation 41A05 Interpolation in approximation theory 41A30 Approximation by other special function classes Keywords:scattered-data interpolation; Euclidean spheres; radial-basis function approximant; spherical-basis function approximant; geodesic distance; interpolation matrix; stability PDFBibTeX XMLCite \textit{F. J. Narcowich} et al., Adv. Comput. Math. 8, No. 3, 137--163 (1998; Zbl 0907.65006) Full Text: DOI