Let f(k) be the Hermite spline interpolant of class C-k and degree 2k + 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 off are known, then fk can be obtained as a sum of f(k-1) and of a particular spline g(k-1) of class Ck- 1 and degree 2k + 1. Beyond the simplicity of the evaluation of 9(k- 1), we prove that it has other interesting properties. We also give some applications of this method in numerical approximation. (c) 2005 Elsevier B.V. All rights reserved.
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