A trivariate near-best blending quadratic quasi-interpolant

On spline quasi-interpolation through dimensions

“…the coefficients functionals are determined by minimizing an upper bound of its infinity norm, derived from the Bernstein-Bézier coefficients of its Lebesgue function. Moreover, an alternative method that combines the blending sum of 1D and 2D QIOs and the near-best approach is proposed in [10]. The above methods allow oversampling.…”

“…where k is a singular, but absolutely integrable function, f is a bounded function for the case (9) and w, f are such that J (w f ; λ) exists for the case (10). Univariate point QIOs are useful tools to construct quadrature formulas both for (9) and for (10).…”

“…where k is a singular, but absolutely integrable function, f is a bounded function for the case (9) and w, f are such that J (w f ; λ) exists for the case (10). Univariate point QIOs are useful tools to construct quadrature formulas both for (9) and for (10). In [25,28,29,35,[39][40][41][42] we generate integration rules based on the approximation of f in (9) or in (10) by point QI splines, we prove a very satisfactory error theory and we provide experimental results.…”

“…In [25,28,29,35,[39][40][41][42] we generate integration rules based on the approximation of f in (9) or in (10) by point QI splines, we prove a very satisfactory error theory and we provide experimental results. By means of product of quadratures such as those obtained for (10), in [27] we construct and study cubature formulas for the numerical evaluation of the following CPV integral: 1) and ( 3), cubatures for the evaluation of integrals…”

“…In particular, the aim of this paper is to collect the main results obtained by the authors, also in collaboration with other researchers, in such a topic, highlighting the approximation properties and the reconstruction of functions and data [3, 5, 6, 8-10, 26, 32-34, 36, 43, 45, 47, 57, 58, 67, 69-71], the applications in numerical integration and differentiation [22, 25, 27-31, 35, 37, 39-42, 44, 56, 68] and the numerical solution of integral and differential problems [2,13,24,38,46]. The above results can also be considered through spline dimension: 1D [2, 13, 25, 28, 29, 35-37, 39-42, 46, 57, 68], 2D [6, 8, 9, 22, 24, 26, 27, 30-34, 38, 43, 45, 56-58, 67, 70] and 3D [3,5,10,44,47,69,71].…”