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.


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