Scattered Data Interpolation on Embedded Submanifolds with Restricted Positive Definite Kernels: Sobolev Error Estimates

@article{Fuselier2012ScatteredDI,
  title={Scattered Data Interpolation on Embedded Submanifolds with Restricted Positive Definite Kernels: Sobolev Error Estimates},
  author={Edward J. Fuselier and Grady B. Wright},
  journal={SIAM J. Numerical Analysis},
  year={2012},
  volume={50},
  pages={1753-1776}
}
In this paper we present error estimates for kernel interpolation at scattered sites on manifolds. The kernels we consider will be obtained by the restriction of positive definite kernels on Rd, such as radial basis functions, to a smooth, compact embedded submanifold M ⊂ Rd with no boundary. For restricted kernels having finite smoothness, we provide a complete characterization of the native space on M. After this and some preliminary setup, we present Sobolev-type error estimates for the… CONTINUE READING
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