Let fkbe the Hermite spline interpolant of class Ckand degree 2 k + 1 to a real function f which is defined by its values and derivatives up to order k at some knots of an interval [a, b]. We present a quite simple recursive method for the construction of fk. We show that if at the step k, the values of the kth derivative of f are known, then fkcan be obtained as a sum of fk-1and of a particular spline gk-1of class Ck-1and degree 2 k + 1. Beyond the simplicity of the evaluation of gk-1, we prove that it has other interesting properties. We also give some applications of this method in numerical approximation. © 2005 Elsevier B.V. All rights reserved.
Mazroui, A., Sbibih, D., & Tijini, A. (2005). A recursive construction of Hermite spline interpolants and applications. Journal of Computational and Applied Mathematics, 183(1), 67–83. https://doi.org/10.1016/j.cam.2005.01.002