Spectral convergence of multiquadric interpolation

Abstract

In this paper, we consider interpolants on h ·ℤ n from the closure of the space spanned by translates of the function (‖·‖ 2 + 1) β/2 (β>− n and not an even nonnegative integer) along h ·ℤ n . We show that these interpolants approximate a function, whose Fourier transform satisfies certain asymptotic conditions, up to an error of order h p , on any compact domain in ℝ n , where p is only restricted by the smoothness of the function.