Direct and Inverse Sobolev Error Estimates for Scattered Data Interpolation via Spherical Basis Functions
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.
radial basis function, sobolev space, target function, reproduce Kernel Hilbert space, native Space
Narcowich, Francis J., Xingping Sun, Joseph D. Ward, and Holger Wendland. "Direct and inverse Sobolev error estimates for scattered data interpolation via spherical basis functions." Foundations of Computational Mathematics 7, no. 3 (2007): 369-390.
Foundations of Computational Mathematics