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Abstract: Bounds are provided on how well functions in Sobolev spaces on the sphere can be approximated by spherical splines, where a spherical spline of degree d is a C r function whose pieces are the restrictions of homogoneous polynomials of degree d to the sphere. The bounds are expressed in terms of appropriate seminorms defined with the help of radial projection, and are obtained using appropriate quasi-interpolation operators. x1. (Update)
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BibTeX entry: (Update)
@misc{ neamtu-approximation,
author = "Marian Neamtu and Larry L. Schumaker",
title = "On the Approximation Order of Splines on Spherical Triangulations",
url = "citeseer.ist.psu.edu/491450.html" }
Citations (may not include all citations):689 The Finite Element Method for Elliptic Problems (context) - Ciarlet - 1978
509 Sobolev Spaces (context) - Adams - 1975
238 The Mathematical Theory of Finite Element Methods (context) - Brenner, Scott - 1994
224 Non-Homogeneous Boundary Value Problems and Applications (context) - Lions, Magenes - 1972
34 the approximation power of bivariate splines - Lai - 1998
29 Nonlinear Analysis on Manifolds (context) - Aubin - 1982
28 Spline interpolation and smoothing on the sphere (context) - Wahba - 1981
26 Stability of optimal order approximation by bivariate spline.. - Chui, Hong et al. - 1995
20 Fitting scattered data on spherelike surfaces using spherica.. - Alfeld, Neamtu et al. - 1996
19 Dimension and local bases of homogeneous spline spaces - Alfeld, Neamtu et al. - 1996
17 On stable local bases for bivariate polynomial spline spaces - Davydov, Schumaker - 2001
16 Constructive Approximation on the Sphere with Applications t.. (context) - Freeden, Gervens et al. - 1998
6 Springer Lecture Notes in Mathematics (context) - Muller - 1966
6 Sobolev Spaces on Riemannian Manifolds (context) - Hebey - 1996
2 Bernstein-B'ezier polynomials on spheres (context) - Alfeld, Neamtu et al. - 1996
1 Local approximation on manifolds using radial functions and .. (context) - Levesley
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