On bivariate osculatory interpolation (Q1184128)

Assume that \(N_{k-1}\) is a set of \(s_{k-1}:=\dim \Pi_{k-1}\) points in \(\mathbb{R}^ 2\) for which the interpolation problem with polynomials in \(\Pi_{k-1}\) is uniquely solvable. Assume that \(\ell\) is a line which does not intersect \(N_{k-1}\). If \(k+1\) points on \(\ell\) are added to \(N_{k-1}\), then a feasible set \(N_ k\) for \(\Pi_ k\) is created. This result on `` straight-line-superposed Lagrangian interpolation'' is extended to osculatory interpolation.