Trivariate near-best blending spline quasi-interpolation operators
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Springer New York LLC
Date
2018-05Referencia bibliográfica
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
Abstract
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.