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For $m,n \in \mathbb{N}$, $m\geq 1$ and a given function $f : \mathbb{R}^m\longrightarrow \mathbb{R}$ the polynomial interpolation problem (PIP) is to determine a \emph{generic node set} $P \subseteq \mathbb{R}^m$ and the coefficients of the uniquely defined polynomial $Q\in\mathbb{R}[x_1,\dots,x_m]$ in $m$ variables of degree $\mathrm{deg}(Q)\leq n \in \mathbb{N}$ that fits $f$ on $P$, i.e., $Q(p) = f(p)$, $\forall\, p \in P$.
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