An algorithm for numerical integration based on quasi-interpolating splines

Quasi-interpolatory splines based on Schoenberg points

“…Convergence results were already proved for product quadrature rules based on QI splines using parameters T 1 − T 5 in [1,[3][4][5]. These convergence results are both for bounded [1,3,4] and unbounded integrands [4].…”

“…These convergence results are both for bounded [1,3,4] and unbounded integrands [4]. Pointwise and uniform convergence results are proved in [1,3,5] for sequences of CPV integrals of these splines. We apply these convergence results to the QI splines based on T 6 .…”

“…We assume that τ ij = τ ik for j = k, so that the divided differences involve only function values. Under this assumption, Q n f can be expressed by [1] …”

“…In several recent papers [1][2][3][4][5] Dagnino et al studied the application of quasiinterpolatory (QI) splines to numerical integration. This class of QI splines, introduced in [6], can be defined, starting with a positive integer p ≥ 2, the order of the spline space, a partition We shall assume throughout this paper that H n → 0 as n → ∞.…”

Numerical integration based on trivariate C 2 quartic spline quasi-interpolants

“…In order to define a box spline, it is necessary to specify a set of directions that determine the shape of its support and also its continuity properties. Following [26], we consider the set X = {e 1 , e 2 , e 3 , e 4 , e 5 , e 6 , e 7 } of seven directions of Z 3 , spanning R 3 , where…”