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Multiscale interpolation on the sphere: Convergence rate and inverse theorem

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  • Li, Ming
  • Cao, Feilong

Abstract

In this paper we study the convergence rate and inverse theorem for spherical multiscale interpolation in Lp and Sobolev norms. The multiscale interpolation is constructed using a sequence of scaled, compactly supported radial basis functions restricted to the unit sphere Sn. For the interpolation scheme the problem called “native space barrier” is considered. In addition, a Bernstein type inequality is established to derive an inverse theorem for the multiscale interpolation, and some numerical experiments to illustrate the theoretical results are given.

Suggested Citation

  • Li, Ming & Cao, Feilong, 2015. "Multiscale interpolation on the sphere: Convergence rate and inverse theorem," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 134-150.
    • Handle: RePEc:eee:apmaco:v:263:y:2015:i:c:p:134-150
    DOI: 10.1016/j.amc.2015.04.032
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    Cited by:

    1. Allasia, Giampietro & Cavoretto, Roberto & De Rossi, Alessandra, 2018. "Hermite–Birkhoff interpolation on scattered data on the sphere and other manifolds," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 35-50.

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