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- P. Sablonnière
- 2003

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)

- Paul Sablonnière
- 2004

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)

- P. Sablonnière
- 2005

We describe some new univariate spline quasi-interpolants on uniform partitions of bounded intervals. Then we give some applications to numerical analysis: integration, differentiation and approximation of zeros.

- Domingo Barrera, María J. Ibáñez, Paul Sablonnière, Driss Sbibih
- J. Computational Applied Mathematics
- 2010

- Paul Sablonnière
- 2005

We study a new simple quadrature rule based on integrating a C 1 quadratic spline quasi-interpolant on a bounded interval. We give nodes and weights for uniform and non-uniform partitions. We also give error estimates for smooth functions and we compare this formula with Simpson's rule.

- Carla Manni, Paul Sablonnière
- Adv. Comput. Math.
- 2007

- Françoise Foucher, Paul Sablonnière
- Mathematics and Computers in Simulation
- 2008

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)

- Paul Sablonnière
- Computer Aided Geometric Design
- 1985

- Françoise Foucher, Paul Sablonnière
- Mathematics and Computers in Simulation
- 2009

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)

- Sara Remogna, Paul Sablonnière
- Computer Aided Geometric Design
- 2011