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A simple method for smoothing functions and compressing Hermite data

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Abstract

Let τ=(a=x0<x1<⋅⋅⋅<xn=b) be a partition of an interval [a,b] of R, and let f be a piecewise function of class Ck on [a,b] except at knots xi where it is only of class \(C^{k_{i}}\) , kik. We study in this paper a novel method which smooth the function f at xi, 0≤in. We first define a new basis of the space of polynomials of degree ≤2k+1, and we describe algorithms for smoothing the function f. Then, as an application, we give a recursive computation of classical Hermite spline interpolants, and we present a method which allows us to compress Hermite data. The most part of these results are illustrated by some numerical examples.

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Correspondence to A. Mazroui.

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Communicated by T.N.T. Goodman

AMS subject classification

41A05, 41A15, 65D05, 65D07, 65D10

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Mazroui, A., Sbibih, D. & Tijini, A. A simple method for smoothing functions and compressing Hermite data. Adv Comput Math 23, 279–297 (2005). https://doi.org/10.1007/s10444-004-1783-y

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  • DOI: https://doi.org/10.1007/s10444-004-1783-y

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