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pro vyhledávání: '"Marcellán, Francisco"'
This paper addresses the challenge of function approximation using Hermite interpolation on equally spaced nodes. In this setting, standard polynomial interpolation suffers from the Runge phenomenon. To mitigate this issue, we propose an extension of
Externí odkaz:
http://arxiv.org/abs/2409.03357
Autor:
Sghaier, Mabrouk, Marcellán, Francisco
Let $\mathcal{T}_{\mu}$ be the Dunkl operator. A pair of symmetric measures $(u, v)$ supported on a symmetric subset of the real line is said to be a symmetric Dunkl-coherent pair if the corresponding sequences of monic orthogonal polynomials $\{P_n\
Externí odkaz:
http://arxiv.org/abs/2405.14771
In this contribution, quasi-orthogonality of polynomials generated by Geronimus and Uvarov transformations is analyzed. An attempt is made to discuss the recovery of the source orthogonal polynomial from the quasi-Geronimus and quasi-Uvarov polynomia
Externí odkaz:
http://arxiv.org/abs/2403.03789
Let $(P_n(x;z;\lambda))_{n\geq 0}$ be the sequence of monic orthogonal polynomials with respect to the symmetric linear functional $\mathbf{s}$ defined by $$\langle\mathbf{s},p\rangle=\int_{-1}^1 p(x)(1-x^2)^{(\lambda-1/2)} e^{-zx^2}dx,\qquad\lambda>
Externí odkaz:
http://arxiv.org/abs/2401.17674
In this contribution we deal with Gaussian quadrature rules based on orthogonal polynomials associated with a weight function $w(x)= x^{\alpha} e^{-x}$ supported on an interval $(0,z)$, $z>0.$ The modified Chebyshev algorithm is used in order to test
Externí odkaz:
http://arxiv.org/abs/2401.00752
Additive perturbations, specifically, matrix Uvarov transformations for matrix orthogonal polynomials, are under consideration. Christoffel-Uvarov formulas are deduced for the perturbed biorthogonal families, along with their matrix norms. These form
Externí odkaz:
http://arxiv.org/abs/2312.05137
We define the family of truncated Laguerre polynomials $P_n(x;z)$, orthogonal with respect to the linear functional $\ell$ defined by $$\langle{\ell,p\rangle}=\int_{0}^zp(x)x^\alpha e^{-x}dx,\qquad\alpha>-1.$$ The connection between $P_n(x;z)$ and th
Externí odkaz:
http://arxiv.org/abs/2307.09581
Autor:
Marcellán, Francisco, Zurrián, Ignacio
In this contribution we deal with sequences of polynomials orthogonal with respect to a Sobolev type inner product. A banded symmetric operator is associated with such a sequence of polynomials according to the higher order difference equation they s
Externí odkaz:
http://arxiv.org/abs/2302.08313
Autor:
Dominici, Diego, Marcellán, Francisco
We classify all the \emph{$\Delta$-}coherent pairs of measures of the second kind on the real line. We obtain $5$ cases, corresponding to all the families of discrete semiclassical orthogonal polynomials of class $s\leq1.$
Comment: 24 pages
Comment: 24 pages
Externí odkaz:
http://arxiv.org/abs/2302.01899