Trivariate near-best blending spline quasi-interpolation operators Barrera Rosillo, Domingo Dagnino, Catterina Ibáñez Pérez, María José Remogna, Sara This work was partially realized during the visiting of the third author to the Department of Mathematics, University of Torino. This work has been partially supported by the program “Progetti di Ricerca 2016” of the Gruppo Nazionale per il Calcolo Scientifico (GNCS) - INdAM. Moreover, the authors thank the University of Torino for its support to their research. First and third authors also thank the Research Group FQM-191 for its support to this research A method to define trivariate spline quasi-interpolation operators (QIOs) is developed by blending univariate and bivariate operators whose linear functionals allow oversampling. In this paper, we construct new operators based on univariate B-splines and bivariate box splines, exact on appropriate spaces of polynomials and having small infinity norms. An upper bound of the infinity norm for a general blending trivariate spline QIO is derived from the Bernstein-Bézier coefficients of the fundamental functions associated with the operators involved in the construction. The minimization of the resulting upper bound is then proposed and the existence of a solution is proved. The quadratic and quartic cases are completely worked out and their exact solutions are explicitly calculated. 2024-01-30T11:05:56Z 2024-01-30T11:05:56Z 2018-05 journal article Barrera, D., Dagnino, C., Ibáñez, M.J. et al. Trivariate near-best blending spline quasi-interpolation operators. Numer Algor 78, 217–241 (2018). https://doi.org/10.1007/s11075-017-0373-2 https://hdl.handle.net/10481/87621 10.1007/s11075-017-0373-2 eng http://creativecommons.org/licenses/by-nc-sa/4.0/ embargoed access Atribución-NoComercial-CompartirIgual 4.0 Internacional Springer New York LLC