Direct and Inverse Sobolev Error Estimates for Scattered Data Interpolation via Spherical Basis Functions |
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| Authors: | Francis J Narcowich Xingping Sun Joseph D Ward Holger Wendland |
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| Institution: | (1) Department of Mathematics, Texas A&M University, College Station, TX 77843, USA;(2) Department of Mathematics, Southwest Missouri State University, Springfield, MO 65804, USA;(3) Universitat Gottingen, Lotzestrasse 16-18, D-37083, Gottingen, Germany |
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| Abstract: | The purpose of this paper is to get error estimates for spherical basis function (SBF) interpolation and approximation for
target functions in Sobolev spaces less smooth than the SBFs, and to show that the rates achieved are, in a sense, best possible.
In addition, we establish a Bernstein-type theorem, where the smallest separation between data sites plays the role of a Nyquist
frequency. We then use these Berstein-type estimates to derive inverse estimates for interpolation via SBFs. |
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