Alicia Cachafeiro

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In this paper we consider a Sobolev inner product (f, g)S = ∫ fgdμ+ λ ∫ f ′g′dμ (1) and we characterize the measures μ for which there exists an algebraic relation between the polynomials, {Pn}, orthogonal with respect to the measure μ and the polynomials, {Qn}, orthogonal with respect to (1), such that the number of involved terms does not depend on the(More)
In this paper we study a quadrature formula for Bernstein–Szegő measures on the unit circle with a fixed number of nodes and unlimited exactness. Taking into account that the Bernstein–Szegő measures are very suitable for approximating an important class of measures we also present a quadrature formula for this type of measures such that the error can be(More)
The aim of this talk is to present some results and ideas related to Hermite interpolation on the unit circle with equally spaced nodal systems. The main topics covered in this overview are the obtention of explicit expressions for the interpolation polynomials, the study of the rate of convergence of the Hermite-Fejér interpolants and other related topics(More)
In this paper we study convergence and computation of interpolatory quadrature formulas with respect to a wide variety of weight functions. The main goal is to evaluate accurately a definite integral, whose mass is highly concentrated near some points. The numerical implementation of this approach is based on the calculation of Chebyshev series and some(More)