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 homogeneous 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.
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Neamtu, M., Schumaker, L.L. On the Approximation Order of Splines on Spherical Triangulations. Advances in Computational Mathematics 21, 3–20 (2004). https://doi.org/10.1023/B:ACOM.0000016430.93487.ec
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DOI: https://doi.org/10.1023/B:ACOM.0000016430.93487.ec