MULTIVARIATE CARDINAL INTERPOLATION WITH RADIAL-BASIS FUNCTIONS

For a radial-basis function φ{symbol}:ℛ→ℛ we consider interpolation on an infinite regular lattice, to f:ℛn→ℛ, where h is the spacing between lattice points and the cardinal function, satisfies X(j)=δoj for all j∈ℒn. We prove existence and uniqueness of such cardinal functions X, and we establish polynomial precision properties of Ih for a class of radial-basis functions which includes {Mathematical expression}, {Mathematical expression}, and {Mathematical expression} where q∈ℒ+. We also deduce convergence orders of Ihf to sufficiently differentiable functions f when h→0. © 1990 Springer-Verlag New York Inc.