A trivariate near-best blending quadratic quasi-interpolant

Abstract

In this paper, we construct a new trivariate spline quasi-interpolation operator. It is expressed as blending sum of univariate and bivariate C1 quadratic spline quasi-interpolants and it is of near-best type, i.e. it has a small infinity norm and the coefficients functionals defining it are determined by minimizing an upper bound of the operator infinity norm, derived from the Bernstein-Bézier coefficients of its Lebesgue function.