Geodesic
Reference points based recursive approximation
Kybernetika, Tome 49 (2013) no. 1, pp. 60-72

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The paper studies polynomial approximation models with a new type of constraints that enable to get estimates with significant properties. Recently we enhanced a representation of polynomials based on three reference points. Here we propose a two-part cubic smoothing scheme that leverages this representation. The presence of these points in the model has several consequences. The most important one is the fact that by appropriate location of the reference points the resulting approximant of two successively assessed neighboring approximants will be smooth. We also show that the considered models provide estimates with appropriate statistical properties such as consistency and asymptotic normality.
Classification : 41A10, 62-07, 62F10, 62J05, 62L12, 65D05, 65D07, 65D10
Keywords: approximation model; consistency; asymptotic normality 
@article{KYB_2013__49_1_a4,
     author = {R\'evayov\'a, Martina and T\"or\"ok, Csaba},
     title = {Reference points based recursive approximation},
     journal = {Kybernetika},
     pages = {60--72},
     publisher = {mathdoc},
     volume = {49},
     number = {1},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2013__49_1_a4/}
}
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Révayová, Martina; Török, Csaba. Reference points based recursive approximation. Kybernetika, Tome 49 (2013) no. 1, pp. 60-72. http://geodesic.mathdoc.fr/item/KYB_2013__49_1_a4/