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.

Trivariate near-best blending spline quasi-interpolation operators

DAGNINO, Catterina;REMOGNA, Sara
2018-01-01

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.
2018
78
217
241
Blending quasi-interpolation, Minimal norm, Bernstein-Bézier coefficients
Barrera, D.; Dagnino, C.; Ibáñez, M. J.; Remogna, S.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1644988
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