Raising the approximation order of multivariate quasi-interpolants

Abstract

Let $${\fancyscript{S}}(\phi _m)$$ be the space generated by a finite set $$\phi _m$$ of continuous functions defined on a domain $$\varOmega $$ in $$\mathbb {R}^s$$ . We suppose that this space contains the space of polynomials of degree at most $$m$$ . By using the blossoming approach, we show how to construct multivariate quasi-interpolants which have important properties such as high order of regularity and polynomial reproduction. The quasi-interpolation coefficients are polynomials, obtained as a blossom of a specific polynomial. We will show that some results existing in the literature can be obtained as particular cases to our method.