2010 **Abstract:** Abstract. We consider discrete quasi-interpolants based on C 1 quadratic boxsplines on uniform criss-cross triangulations of a rectangular domain. The main problem consists in finding good (if not best) coefficient functionals, associated with boundary box-splines, giving both an optimal approximation order and a small infinity norm of the operator. Moreover, we want that these functionals only involve data points inside the domain. They are obtained either by minimizing their infinity norm w.r.t. a finite num…

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“…This can increase the value of the infinity norm of the quasiinterpolant and eventually give some trouble in numerical computations. For that reason, we shall develop in a further paper alternative functionals having larger supports and lower infinity norms (as is done in the corresponding work by Sara Remogna [25] on quadratic spline QIs).…”

confidence: 98%

“…This can increase the value of the infinity norm of the quasiinterpolant and eventually give some trouble in numerical computations. For that reason, we shall develop in a further paper alternative functionals having larger supports and lower infinity norms (as is done in the corresponding work by Sara Remogna [25] on quadratic spline QIs).…”

confidence: 98%

“…The simplest one, S 1 , is a bivariate extension of the Schoenberg-Marsden operator (Chui and Wang, 1984;Sablonnière, 2003a,b). The other two kinds of operators, constructed in Remogna (2010a), are related to the operator S 2 , proposed in Sablonnière (2003a,b), exact on P 2 [x, y] and obtained from (6) by replacing the Laplacian ∆ by its five points discretisation. The operator S 2 has the form…”

confidence: 99%

“…Using the method presented in [19], we are interested in the construction of two different types of discrete quasi-interpolants…”

confidence: 99%

“…The method used in this subsection is closely related to the techniques given in [1][2][3]17] to define near-best discrete quasi-interpolants on type-1 and type-2 triangulations (see also [4,19,21]). …”

confidence: 99%