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On condition numbers associated with radial-function interpolation. (English) Zbl 0813.65005

Estimates on spectral condition numbers for scattered-data interpolation matrices associated with a certain class of conditionally positive definite radial functions of order 0, including the Gaussians, are provided. In addtion \(l^ p\)-condition number estimates, with \(1 \leq p < \infty\), are discussed. The estimates on the spectral condition numbers lead to necessary and sufficient conditions for such condition numbers to be independent of the number of data sites.

MSC:

65D05 Numerical interpolation
65F35 Numerical computation of matrix norms, conditioning, scaling
15A12 Conditioning of matrices
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