On Power Functions and Error Estimates for Radial Basis Function Interpolation
نویسندگان
چکیده
منابع مشابه
Error estimates and condition numbers for radial basis function interpolation
For interpolation of scattered multivariate data by radial basis functions, an \uncertainty relation" between the attainable error and the condition of the interpolation matrices is proven. It states that the error and the condition number cannot both be kept small. Bounds on the Lebesgue constants are obtained as a byproduct. A variation of the Narcowich{Ward theory of upper bounds on the norm...
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We introduce a class of matrix-valued radial basis functions (RBFs) of compact support that can be customized, e.g. chosen to be divergence-free. We then derive and discuss error estimates for interpolants and derivatives based on these matrixvalued RBFs.
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We consider error estimates for the interpolation by a special class of compactly supported radial basis functions. These functions consist of a univariate polynomial within their support and are of minimal degree depending on space dimension and smoothness. Their associated \native" Hilbert spaces are shown to be norm-equivalent to Sobolev spaces. Thus we can derive approximation orders for fu...
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Radial basis function interpolation refers to a method of interpolation which writes the interpolant to some given data as a linear combination of the translates of a single function and a low degree polynomial. We develop an error analysis which works well when the Fourier transform of has a pole of order 2m at the origin and a zero at 1 of order 2 . In case 0 m , we derive error estimates whi...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1998
ISSN: 0021-9045
DOI: 10.1006/jath.1997.3118