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Schaback, Robert

Error estimates and condition numbers for radial basis function interpolation. (English) Zbl 0861.65007

Adv. Comput. Math. 3, No. 3, 251-264 (1995).
Summary: 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 of the inverse of the interpolation matrix is presented in order to handle the whole set of radial basis functions that are currently in use.

Cited in 1 Review
Cited in 291 Documents

MSC:

65D05 Numerical interpolation
41A63 Multidimensional problems
41A05 Interpolation in approximation theory
41A30 Approximation by other special function classes

Keywords:

uncertainty relation; interpolation; scattered multivariate data; radial basis functions; condition number; Lebesgue constants; Narcowich-Ward theory; interpolation matrix
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\textit{R. Schaback}, Adv. Comput. Math. 3, No. 3, 251--264 (1995; Zbl 0861.65007)
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References:

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