In previous papers the convergence of sequences of``rectangular'' multivariate Pade-type approxim... more In previous papers the convergence of sequences of``rectangular'' multivariate Pade-type approximants was studied. In other publications definitions of`t riangular'' multivariate Pade-type approximants were given. We extend these results to the general order definition where the choice of the denominator polynomial is completely free. Also we develop convergence theorems and we distinguish between results obtained in polydiscs and in multivariate balls. The numerical examples section illustrates this difference and compares the obtained results with the approximation power of general order multivariate Pade approximants.
Journal of Computational and Applied Mathematics, 2015
OrthoQuad 2014 was an international symposium on orthogonality, quadrature, and related topics, h... more OrthoQuad 2014 was an international symposium on orthogonality, quadrature, and related topics, held on January 20-24, 2014 in Puerto de la Cruz, Tenerife, Spain. It was held in memory of Professor Pablo González-Vera (1955.
Journal of Mathematical Analysis and Applications, 2011
We study the asymptotic zero distribution of the rescaled Laguerre polynomials, L (αn) n (nz), wi... more We study the asymptotic zero distribution of the rescaled Laguerre polynomials, L (αn) n (nz), with the parameter α n varying in such a way that lim n→∞ α n /n = −1. The connection with the so-called Szegö curve will be showed.
Journal of Computational and Applied Mathematics, 1994
... Appl. Math. 32 (1 & 2) (1990) 97-105. [6] E. Hendriksen, Moment methods i... more ... Appl. Math. 32 (1 & 2) (1990) 97-105. [6] E. Hendriksen, Moment methods in two-point Pad approximation, J. Approx. Theory 40 (1984) 313-326. [7] E. Hendriksen and H. van Rossum, Moment methods and Pad approximation: The unitary case, J. Math. Anal. Appl. ...
In previous papers the convergence of sequences of``rectangular'' multivariate Pade -type approxi... more In previous papers the convergence of sequences of``rectangular'' multivariate Pade -type approximants was studied. In other publications definitions of`t riangular'' multivariate Pade -type approximants were given. We extend these results to the general order definition where the choice of the denominator polynomial is completely free. Also we develop convergence theorems and we distinguish between results obtained in polydiscs and in multivariate balls. The numerical examples section illustrates this difference and compares the obtained results with the approximation power of general order multivariate Pade approximants.
Classical Jacobi polynomials Pn(α,β), with α,β>-1α,β>-1, have a number of well-known properties, ... more Classical Jacobi polynomials Pn(α,β), with α,β>-1α,β>-1, have a number of well-known properties, in particular the location of their zeros in the open interval (-1,1)(-1,1). This property is no longer valid for other values of the parameters; in general, zeros are complex. In this paper we study the strong asymptotics of Jacobi polynomials where the real parameters αn,βnαn,βn depend on n in such a way thatThe non-hermitian orthogonality relations for Jacobi polynomials with varying parameters lie in the core of our approach; in the cases we consider, these relations hold on a single contour of the complex plane. The asymptotic analysis is performed using the Deift–Zhou steepest descent method based on the Riemann–Hilbert reformulation of Jacobi polynomials.
In previous papers the convergence of sequences of``rectangular'' multivariate Pade-type approxim... more In previous papers the convergence of sequences of``rectangular'' multivariate Pade-type approximants was studied. In other publications definitions of`t riangular'' multivariate Pade-type approximants were given. We extend these results to the general order definition where the choice of the denominator polynomial is completely free. Also we develop convergence theorems and we distinguish between results obtained in polydiscs and in multivariate balls. The numerical examples section illustrates this difference and compares the obtained results with the approximation power of general order multivariate Pade approximants.
Journal of Computational and Applied Mathematics, 2015
OrthoQuad 2014 was an international symposium on orthogonality, quadrature, and related topics, h... more OrthoQuad 2014 was an international symposium on orthogonality, quadrature, and related topics, held on January 20-24, 2014 in Puerto de la Cruz, Tenerife, Spain. It was held in memory of Professor Pablo González-Vera (1955.
Journal of Mathematical Analysis and Applications, 2011
We study the asymptotic zero distribution of the rescaled Laguerre polynomials, L (αn) n (nz), wi... more We study the asymptotic zero distribution of the rescaled Laguerre polynomials, L (αn) n (nz), with the parameter α n varying in such a way that lim n→∞ α n /n = −1. The connection with the so-called Szegö curve will be showed.
Journal of Computational and Applied Mathematics, 1994
... Appl. Math. 32 (1 & 2) (1990) 97-105. [6] E. Hendriksen, Moment methods i... more ... Appl. Math. 32 (1 & 2) (1990) 97-105. [6] E. Hendriksen, Moment methods in two-point Pad approximation, J. Approx. Theory 40 (1984) 313-326. [7] E. Hendriksen and H. van Rossum, Moment methods and Pad approximation: The unitary case, J. Math. Anal. Appl. ...
In previous papers the convergence of sequences of``rectangular'' multivariate Pade -type approxi... more In previous papers the convergence of sequences of``rectangular'' multivariate Pade -type approximants was studied. In other publications definitions of`t riangular'' multivariate Pade -type approximants were given. We extend these results to the general order definition where the choice of the denominator polynomial is completely free. Also we develop convergence theorems and we distinguish between results obtained in polydiscs and in multivariate balls. The numerical examples section illustrates this difference and compares the obtained results with the approximation power of general order multivariate Pade approximants.
Classical Jacobi polynomials Pn(α,β), with α,β>-1α,β>-1, have a number of well-known properties, ... more Classical Jacobi polynomials Pn(α,β), with α,β>-1α,β>-1, have a number of well-known properties, in particular the location of their zeros in the open interval (-1,1)(-1,1). This property is no longer valid for other values of the parameters; in general, zeros are complex. In this paper we study the strong asymptotics of Jacobi polynomials where the real parameters αn,βnαn,βn depend on n in such a way thatThe non-hermitian orthogonality relations for Jacobi polynomials with varying parameters lie in the core of our approach; in the cases we consider, these relations hold on a single contour of the complex plane. The asymptotic analysis is performed using the Deift–Zhou steepest descent method based on the Riemann–Hilbert reformulation of Jacobi polynomials.
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