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A note on stability results for scattered data interpolation on Euclidean spheres

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Abstract

The present work considers the interpolation of the scattered data on the d-sphere by spherical polynomials. We prove bounds on the conditioning of the problem which rely only on the separation distance of the sampling nodes and on the degree of polynomials being used. To this end, we establish a packing argument for well separated sampling nodes and construct strongly localized polynomials on spheres. Numerical results illustrate our theoretical findings.

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Authors and Affiliations

  1. Department of Mathematics, Chemnitz University of Technology, 09107, Chemnitz, Germany

    Stefan Kunis

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  1. Stefan Kunis
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Correspondence to Stefan Kunis.

Additional information

Communicated by Joe Ward.

Dedicated to Professor Manfred Tasche on the occasion of his 65th birthday.

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Kunis, S. A note on stability results for scattered data interpolation on Euclidean spheres. Adv Comput Math 30, 303–314 (2009). https://doi.org/10.1007/s10444-008-9069-4

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  • DOI: https://doi.org/10.1007/s10444-008-9069-4

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