Let be a triangulation of some polygonal domain in R 2 and S r k ((), the space of all bivariate C r piecewise polynomials of total degree k on. In this paper, we construct a local basis of some subspace of the space S r k ((), where k 3r+2, that can be used to provide the highest order of approximation, with the property that the approximation constant of… (More)
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The problem of multivariate polynomial interpolation is very old. Among the papers published during the last decade, we only include 1-16] in the References. Let N s n = ? n+s s. The problem can be stated as follows: study the location of nodes (or sample points) fx i : i = 1; : : : ; N s n g in R s such that for every data ff i : i = 1; : : : ; N s n g,… (More)
Let be a linear combination of certain box splines and ^ its Fourier transform, such that ^ (0) 6 = 0 and D ^ (2k) = 0 for all k 2 Z N nf0g and. In this paper we construct an expression of the multivariate polynomial (? y) in terms of a linear combination of the integer translates of (), where the coeecients can be computed recursively using only the… (More)
Let ∆ be a triangulation of some polygonal domain in IR 2 and S r k (∆) the space of all bivariate C r piecewise polynomials of total degree ≤ k on ∆. The approximation order of S r k (∆) is defined to be the largest real number ρ for which dist(f, S r k (∆)) ≤ Const |∆| ρ for all sufficiently smooth functions f , where the distance is measured in the… (More)
Explicit formulae, in terms of Bernstein-Bézier coefficients, of the Fourier transform of bivariate polynomials on a triangle and univariate polynomials on an interval are derived in this paper. Examples are given and discussed to illustrate the general theory. Finally, this consideration is related to the study of refinement masks of spline function… (More)