Interpolation systems in \(R^ k\) (Q801489)

In a previous paper [Numer. Math. 39, 1-14 (1982; Zbl 0457.65004)] the first author and \textit{J. I. Maeztu} used a geometrical method to construct a set of data of interpolation and a polynomial interpolating space from an interpolation system in \(R^ k\) (k\(\geq 2)\). The solution of the problem was given in the Newton form. In this paper those results are extended in such a way that the interpolating space is not necessarily a polynomial and furthermore a weight (0 or 1) is associated to each point of the interpolation system to enlarge the flexibility of the method. In the new results the case \(k=1\) is also included.