Paul Sablonnière

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We study some C 1 quadratic spline quasi-interpolants on bounded domains ⊂ R d , d = 1, 2, 3. These operators are of the form Q f (x) = k∈K (() µ k (f)B k (x), where K (() is the set of indices of B-splines B k whose support is included in the domain and µ k (f) is a discrete linear functional based on values of f in a neighbourhood of x k ∈ supp(B k). The(More)
Polynomial and spline quasi-interpolants (QIs) are practical and effective approximation operators. Among their remarkable properties, let us cite for example: good shape properties, easy computation and evaluation (no linear system to solve), uniform boundedness independently of the degree (poly-nomials) or of the partition (splines), good approximation(More)
Given a bivariate function f defined in a rectangular domain Ω, we approximate it by a C1 quadratic spline quasi-interpolant (QI) and we take partial derivatives of this QI as approximations to those of f. We give error estimates and asymptotic expansions for these approximations. We also propose a simple algorithm for the determination of stationary(More)
Univariate and multivariate quadratic spline quasi-interpolants provide interesting approximation formulas for derivatives of approximated functions that can be very accurate at some points thanks to the superconvergence properties of these operators. Moreover, they also give rise to good global approximations of derivatives on the whole domain of(More)