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Sloan, Ian H; Wendland, Holger (2009)
Publisher: American Mathematical Society
Languages: English
Types: Article

Classified by OpenAIRE into

ACM Ref: ComputingMethodologies_COMPUTERGRAPHICS
Interpolation by radial basis functions and interpolation by polynomials are both popular methods for function reconstruction from discrete data given on spheres. Recently, there has been an increasing interest in employing these function families together in hybrid schemes for scattered data modeling and the solution of partial differential equations on spheres. For the theoretical analysis of numerical methods for the associated discretized systems, a so-called inf-sup condition is crucial. In this paper, we derive such an inf-sup condition, and show that the constant in the infsup condition is independent of the polynomial degree and of the chosen point set, provided the mesh norm of the point set is sufficiently small. We then use the inf-sup condition to derive a new error analysis for the hybrid interpolation scheme of Sloan and Sommariva
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    • [12] H. Wendland, Scattered Data Approximation, Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, Cambridge, UK, 2005. MR2131724 (2006i:41002) School of Mathematics and Statistics, University of New South Wales, Sydney, NSW, 2052, Australia E-mail address:
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