O. Nouisser

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In this paper we present a study of spaces of splines in C k (R 2) with supports the square Σ1 and the lozenge Λ1 formed respectively by four and eight triangles of the uniform four directional mesh of the plane. Such splines are called Σ1 and Λ1-splines. We first compute the dimension of the space of Σ1-splines. Then we prove the existence of a unique(More)
In this paper, we construct a local quasi-interpolant Q for fitting a function f defined on the sphere S. We first map the surface S onto a rectangular domain and next, by using the tensor product of polynomial splines and 2π-periodic trigonometric splines, we give the expression of Qf. The use of trigonometric splines is necessary to enforce some boundary(More)
In this paper, we show how by a very simple modification of bivariate spline discrete quasi-interpolants, we can construct a new class of quasi-interpolants, which have remarkable properties such as high order of regularity and polynomial reproduction. More precisely, given a spline discrete quasi-interpolation operator Qd, which is exact on the space Pm of(More)
In this paper, we propose several approximations of a multivariate function by quasiinterpolants on non-uniform data and we study their properties. In particular, we characterize those that preserve constants via the partition of unity approach. As one of the main results, we show how by a very simple modification of a given quasi-interpolant it is possible(More)
Given a B-spline M on R, s≥ 1 we consider a classical discrete quasi-interpolant Qd written in the form Qdf = ∑ i∈Zs f (i)L(· − i), where L(x) :=∑ j∈JcjM(x− j) for some finite subset J ⊂ Z and cj ∈R. This fundamental function is determined to produce a quasi-interpolation operator exact on the space of polynomials of maximal total degree included in the(More)
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