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)
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.
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.
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)