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In this paper, we show how by a very simple modification of bivariate spline discrete quasi-interpolants, we can construct a new class of quasi-interpolants, which have remarkable properties such as high order of regularity and polynomial reproduction. More precisely, given a spline discrete quasi-interpolation operator Q d , which is exact on the space P m(More)
In this paper, we propose several approximations of a multivariate function by quasiinterpolants on non-uniform data and we study their properties. In particular, we characterize those that preserve constants via the partition of unity approach. As one of the main results, we show how by a very simple modification of a given quasi-interpolant it is possible(More)
Given a B-spline M on R s , s ≥ 1 we consider a classical discrete quasi-interpolant Q d written in the form Q d f = i ∈ Z s f (i)L(· − i), where L(x) := j∈J c j M(x − j) for some finite subset J ⊂ Z s and c j ∈ R. This fundamental function is determined to produce a quasi-interpolation operator exact on the space of polynomials of maximal total degree(More)
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