B. Della Vecchia

Pointwise simultaneous approximation by rational operators

Abstract We obtain pointwise simultaneous approximation estimates for rational operators which are not possible by algebraic polynomials.

Saturation of the Shepard operators

We discuss the Shepard operators Sn (f; x) in this paper and establish the saturation of the sequence {Snf}n-1∞, as well as investigate some related questions.

Direct and converse results by rational operators

We give direct and converse theorems for rational approximation by Shepard operators.

Approximation of the Hilbert Transform on the real semiaxis using Laguerre zeros

The authors propose two new algorithms for the computation of Cauchy principal value integrals on the real semiaxis. The proposed quadrature rules use zeros of Laguerre polynomials. Theoretical error estimates are proved and some numerical examples are showed.

Approximation with exponential weights in (−1, 1)

Abstract We construct Shepard-type operators for weighted uniform approximation of functions with endpoint singularities by exponential-type weights in [−1,1]. Convergence theorems and pointwise and uniform approximation error estimates not possible by polynomials are proved.

Weighted approximation of functions on the real line by Bernstein polynomials

The authors give error estimates, a Voronovskaya-type relation, strong converse results and saturation for the weighted approximation of functions on the real line with Freud weights by Bernstein-type operators.

Hermite interpolation and mean convergence of its derivatives

Weighted Lp convergence of derivatives of Hermite, interpolation on the zeros of Jacobi polynomials plus additional points is investigated.

Approximation of the hilbert transform on the real line using Hermite zeros

The authors study the Hilbert Transform on the real line. They introduce some polynomial approximations and some algorithms for its numerical evaluation. Error estimates in uniform norm are given.

On Functions Approximation by Shepard-Type Operators — A Survey

The authors give a collection of recent results on functions approximation by Shepard-type operators.

Generalized Bernstein polynomials with Pollaczek weight

Bernstein polynomials are a useful tool for approximating functions. In this paper, we extend the applicability of this operator to a certain class of locally continuous functions. To do so, we consider the Pollaczek weight w(x)@?exp(-1x(1-x)),0