Direct and Inverse Sobolev Error Estimates for Scattered Data Interpolation via Spherical Basis Functions

Francis J. Narcowich; Xingping Sun; Joseph D. Ward; Holger Wendland

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Direct and Inverse Sobolev Error Estimates for Scattered Data Interpolation via Spherical Basis Functions

机译：通过球基函数进行散乱数据插值的Sobolev误差正负估计

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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.

机译：本文的目的是在Sobolev空间不如SBF平滑的情况下获得球基函数（SBF）插值的误差估计和目标函数的近似值，并从某种意义上证明所获得的速率是最佳的。此外，我们建立了一个伯恩斯坦型定理，其中数据站点之间的最小间隔起着奈奎斯特频率的作用。然后，我们使用这些Berstein型估计来得出通过SBF进行插值的逆估计。

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《Foundations of Computational Mathematics》 |2007年第3期|369-390|共22页
作者
Francis J. Narcowich; Xingping Sun; Joseph D. Ward; Holger Wendland;
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Department of Mathematics Texas AampampM University College Station TX 77843 USA;

Department of Mathematics Southwest Missouri State University Springfield MO 65804 USA;

Department of Mathematics Texas AampampM University College Station TX 77843 USA;

Universitat Gottingen Lotzestrasse 16-18 D-37083 Gottingen Germany;

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1. Direct and inverse Sobolev error estimates for scattered data interpolation via spherical basis functions [J] . Narcowich FJ, Sun XP, Ward JD, Foundations of computational mathematics . 2007,第3期

机译：通过球基函数对分散数据进行插值的Sobolev误差的直接和反向估计
2. Sobolev Error Estimates and a Bernstein Inequality for Scattered Data Interpolation via Radial Basis Functions [J] . Francis J. Narcowich, Joseph D. Ward, Holger Wendland Constructive Approximation . 2006,第2期

机译：径向基函数的分散数据插值的Sobolev误差估计和Bernstein不等式
3. Scattered-data interpolation on R-n: Error estimates for radial basis and band-limited functions [J] . Narcowich FJ, Ward JD SIAM Journal on Mathematical Analysis . 2004,第1期

机译：R-n上的分散数据插值：径向基和带限函数的误差估计
4. Basis Functions for Scattered Data Quasi-Interpolation [C] . Nira Gruberger, David Levin International Conference on Curves and Surfaces . 2015

机译：分散数据准插值的基本函数
5. MULTIVARIATE INTERPOLATION (CARDINAL BASIS, POLYNOMIAL, TRIANGLE, TETRAHEDRON, SCATTERED DATA) [D] . RESCORLA, KIM L. 1985

机译：多元插值（基数，多项式，三角形，四面体，散射数据）
6. Interpolation Error Estimates for Mean Value Coordinates over Convex Polygons [O] . Alexander Rand, Andrew Gillette, Chandrajit Bajaj -1

机译：凸多边形均值坐标的插值误差估计
7. Error estimates for interpolation of rough data using the scattered shifts of a radial basis function [O] . Brownlee, R. A. 2007

机译：使用散乱的内容粗略数据插值的误差估计径向基函数的移位
8. Interpolation of scattered temperature data measurements onto a worldwide regular grid using radial basis functions with applications to global warming [R] . Kansa, E. J. , Axelrod, M. C. , Kercher, J. R. 1994

机译：使用径向基函数将散射温度数据测量值插值到全球规则网格上，并应用于全球变暖

Direct and Inverse Sobolev Error Estimates for Scattered Data Interpolation via Spherical Basis Functions

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