A constructive approach to nodal splines (Q875177)

The main result is to show that, for a strictly increasing knot sequence, the nodal splines introduced by \textit{J. M. de Villiers} and \textit{C. H. Rohwer} [ibid. 18, 107--119 (1987; Zbl 0637.41009)] can be expressed as linear combinations of the fundamental functions for Hermite-Martensen interpolation [cf. \textit{E. Martensen}, Numer. Math. 21, 70--80 (1973; Zbl 0264.65021)]. The proof is obtained via a discretized version of the Martensen spline interpolation operator. The representations of nodal splines in terms of the Hermite-Martensen basis are compared with the usual B-spline representations. An application of this approach to the construction of symmetric nodal splines of odd degree is also given.