Error estimates for interpolation of rough data using the scattered shifts of a radial basis function
RA Brownlee - Numerical Algorithms, 2005 - Springer
Numerical Algorithms, 2005•Springer
The error between appropriately smooth functions and their radial basis function
interpolants, as the interpolation points fill out a bounded domain in R d, is a well studied
artifact. In all of these cases, the analysis takes place in a natural function space dictated by
the choice of radial basis function–the native space. The native space contains functions
possessing a certain amount of smoothness. This paper establishes error estimates when
the function being interpolated is conspicuously rough.
interpolants, as the interpolation points fill out a bounded domain in R d, is a well studied
artifact. In all of these cases, the analysis takes place in a natural function space dictated by
the choice of radial basis function–the native space. The native space contains functions
possessing a certain amount of smoothness. This paper establishes error estimates when
the function being interpolated is conspicuously rough.
Abstract
The error between appropriately smooth functions and their radial basis function interpolants, as the interpolation points fill out a bounded domain in Rd, is a well studied artifact. In all of these cases, the analysis takes place in a natural function space dictated by the choice of radial basis function – the native space. The native space contains functions possessing a certain amount of smoothness. This paper establishes error estimates when the function being interpolated is conspicuously rough.
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