Multi-degree Tchebycheffian splines are splines with pieces drawn from extended (complete) Tchebycheff spaces, which may differ from interval to interval, and possibly of different dimensions. These are a natural extension of multi-degree polynomial splines. Under quite mild assumptions, they can be represented in terms of a so-called multi-degree Tchebycheffian B-spline (MDTB-spline) basis; such basis possesses all the characterizing properties of the classical polynomial B-spline basis. We… Expand

In this paper, a cubic Hermite spline interpolating scheme reproducing both linear polynomials and hyperbolic functions is considered. The interpolating scheme is mainly defined by means of integral… Expand

This work describes a simple algorithmic construction of a set of basis functions for the space of multi-degree splines with similar properties to standard B-splines, and relies on an extraction operator that represents all MDB-spline as linear combinations of local B- splines of different degrees.Expand

Originally, Tchebycheean B-splines have been deened by generalized divided diierences. In this paper, we deene Tchebycheean B-splines by integration. Based upon this deenition, all basic algorithms… Expand