Sensitivity of RBF interpolation on an otherwise uniform grid with a point omitted or slightly shifted

Authors:
John P. Boyd;Lauren R. Bridge
Affiliations:
Department of Atmospheric, Oceanic and Space Science and Laboratory for Scientific Computation, University of Michigan, 2455 Hayward Avenue, Ann Arbor, MI 48109, United States;Department of Atmospheric, Oceanic and Space Science and Laboratory for Scientific Computation, University of Michigan, 2455 Hayward Avenue, Ann Arbor, MI 48109, United States
Venue:
Applied Numerical Mathematics
Year:
2010

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Abstract

Radial basis functions are popular for interpolation on a scattered or irregular grid. However, theory for an irregular grid is mostly limited to proofs of convergence. Here, we present theory and numerical experiments for two specific cases. The first is an otherwise uniform grid of spacing h in which one point is shifted by an amount sh. The second is a uniform grid with one point omitted. We discuss Gaussian, hyperbolic secant, and inverse quadratic RBFs.