Let fk be the Hermite spline interpolant of class Ck and 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 fk can be obtained as a sum of fk-1 and of a particular spline gk-1 of class Ck-1 and 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.
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