Stanisław Lewanowicz

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Let fP n (x)g 1 n=0 and fQ m (x)g 1 m=0 be two families of orthogonal polynomials. The linearization problem involves only one family via the relation: P i (x) P j (x) = i+j X k=ji?jj L ijk P k (x) and the connection problem mixes both families: P n (x) = n X m=0 C m (n) Q m (x): In many cases, it is possible to build a recurrence relation involving only m(More)
We propose a novel approach to the problem of polynomial approximation of rational Bézier triangular patches with prescribed boundary control points. The method is very efficient thanks to using recursive properties of the bivariate dual Bernstein polynomials and applying a smart algorithm for evaluating a collection of two-dimensional integrals. Some(More)
Extending the results of [1] (see also [2]), we introduce the polynomials of the vector variable x ∈ R d , depending on two parameters q and ω, which generalize the classical multivariate Bernstein polynomials. For ω = 0, we obtain an extension of univariate q-Bernstein polynomials, recently introduced by Phillips [3]. Among the properties of the new(More)
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