On Condition Numbers Associated with Radial-Function Interpolation

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 addition, ℓp-condition number estimates, with 1 ≤ p ≤ ∞ 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.