Konstruktion und algebraische Eigenschaften vonM-Spline-Interpolierenden

Summary This paper generates interpolatingM-splines in the sense of Lucas J. of Approx. Th. 5, 1–14 (1972)] by a simple algebraic construction. The method yieldsM-spline interpolants for every finite family of functionals commuting with the remainder term of a generalized Taylor formula. These assumptions are fulfilled for a large class of spline interpolation problems (e.g. splines generated by certain singular differential operators and splines of several variables) without any further requirements about the geometrical distribution or denseness of the interpolation points. A generalization ofB-splines is used to improve the numerical behaviour of the interpolation process.