OICC Press International Journal of Mathematical Modelling & Computations 2228-6233 2 4 2016 09 22 HIERARCHICAL COMPUTATION OF HERMITE SPHERICAL INTERPOLANT 247 259 EN A. Lamnii Faculty of Science and Technology, University Hassan first, Settat, Morocco Morocco H. Mraoui Journal Article 2016 09 22 In this paper, we propose to extend the hierarchical bivariateHermite Interpolant to the spherical case. Let $T$ be an arbitraryspherical triangle of the unit sphere $S$ and let $u$ be a functiondefined over the triangle $T$. For $k\in \mathbb{N}$, we consider aHermite spherical Interpolant problem $H_k$ defined by some datascheme $\mathcal{D}_k(u)$ and which admits a unique solution $p_k$in the space $B_{n_k}(T)$ of homogeneous Bernstein-B\'ezierpolynomials of degree $n_k=2k$ (resp. $n_k=2k+1$) defined on $T$. Wediscuss the case when the data scheme $\mathcal{D}_{r}(u)$ arenested, i.e., $\mathcal{D}_{r-1}(u)\subset \mathcal{D}_{r}(u)$ forall $1 \leq r \leq k$. This, give a recursive formulae to computethe polynomial $p_k$. Moreover, this decomposition give a new basisfor the space $B_{n_k}(T)$, which are the hierarchical structure.The method is illustrated by a simple numerical example.