The approximation order of four-point interpolatory curve subdivision (Q651102)

The paper is devoted to a modification of the subdivision scheme of \textit{S. Dubuc} [J. Math. Anal. Appl. 114, 185--204 (1986; Zbl 0615.65005)] for interpolating a sequence of data values of a given function from \(\mathbb R\) to \(\mathbb R^d\) with some \(d\geq 1\). Whereas Dubuc's original scheme only works well if the data points are regularly spaced, this new modified version also converges with a high order in the case of irregularly spaced points.