Nearly optimal interpolation of data in $C^2({\mathbb{R}}^2)$. Part I

Abstract

Given $ϵ>0$, we compute a function taking prescribed values at $N$ given points in ${\mathbb{R}}^2$, whose $C^2$-norm is within a factor $(1+ϵ)$ of least possible. The computation takes $C(ϵ)N\log N$ computer operations.