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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 B-splines Bk whose support is included in the domain and μk( f ) is a discrete linear functional based on values of f in a neighbourhood of xk ∈ supp(Bk). The… (More)
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.
The behaviour of four algorithms accelerating the convergence of a subset of LOG is compared (LOG is the set of logarithmic sequences). This subset, denoted LOGF 1 ′ , is that of fixed point sequences whose associated error sequence,e n =S n −S, verifiese n+1 =e n + α2 e n 2 + α3 e n 3 +... , where α3 ≠ α 2 2 , α2 < 0. The algorithms are modifications of… (More)
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 give error estimates for smooth functions and we compare this formula with Simpson’s rule.
Let r be the triangulation generated by a uniform three direction mesh of the plane. Let r6 be the Powell-Sabin subtriangulation obtained by subdividing each triangle T E r by connecting each vertex to the midpoint of the opposite side. Given a smooth function u, we construct a piecewise polynomial function v E G'r(R 2) of degree n = 2r (resp. 2r + 1) for r… (More)
In this paper we address the problem of constructing quasi-interpolants in the space of quadratic Powell-Sabin splines on nonuniform triangulations. Quasi-interpolants of optimal approximation order are proposed and numerical tests are presented.
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 (polynomials) or of the partition (splines), good approximation… (More)