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- Paul 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… (More)

- Paul Sablonnière
- 2003

- Paul Sablonnière
- 2003

We study some C1 quadratic spline quasi-interpolants on bounded domains ⊂ Rd, d = 1, 2, 3. These operators are of the form Q f (x) = ∑ k∈K () μk( f )Bk(x), where K () is the set of indices of… (More)

- Paul Sablonnière
- Adv. Comput. Math.
- 2004

Bernstein bases, control polygons and corner-cutting algorithms are defined for C1 Merrien's curves introduced in [7]. The convergence of these algorithms is proved for two specific families of… (More)

We propose a local solution for the problem of interpolating monotone data by monotone C 2 cubic splines with two additional knots per interval, on an arbitrary partition, and with an approximation… (More)

- Chafik Allouch, Paul Sablonnière, Driss Sbibih, M. Tahrichi
- J. Computational Applied Mathematics
- 2010

Quadrature formulae are established for product integration rules based on discrete spline quasi-interpolants on a bounded interval. The integrand considered may have algebraic or logarithmic… (More)

- Paul Sablonnière
- 1999

Most of the best known positive linear operators are isomorphisms of the maximal subspace of polynomials that they preserve. We give here the differential forms of these isomorphisms and of their… (More)

- Paul Sablonnière
- 2007

We study a new simple quadrature rule based on integrating a C1 quadratic spline quasi-interpolant on a bounded interval. We give nodes and weights for uniform and non-uniform partitions. We also… (More)

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

Given a bivariate function f defined in a rectangular domain @W, we approximate it by a C^1 quadratic spline quasi-interpolant (QI) and we take partial derivatives of this QI as approximations to… (More)

- Paul Sablonnière
- 1978

Abstract Parametrized polynomial spline curves are defined by an S-polygon, but locally they are Bezier curves defined by a B-polygon. Two algorithms are given which construct one polygon from the… (More)