We give algorithms to compute a function $F$ on $\mathbb R^n$, having prescribed Taylor polynomials (or taking prescribed values) at $N$ given points, with the $C^m$-norm of $F$ close to least possible.
"The $C^m$ Norm of a Function with Prescribed Jets II." Rev. Mat. Iberoamericana 25 (1) 275 - 421, March, 2009.