Convergence of multipoint Padé-type approximants

22 pages, no figures.-- MSC2000 code: 41A21.MR#: MR1820896 (2002a:41014)Zbl#: Zbl 0982.41008Let μ be a finite positive Borel measure whose support is a compact subset K of the real line and let I be the convex hull of K. Let r denote a rational function with real coefficients whose poles lie in \bbfC\setminus I\$ and r(\infty)=0$. We consider multipoint rational interpolants of the function$$f(z)=\int {d\mu(x)\over z-x}+r(z)$$, where some poles are fixed and others are left free. We show that if the interpolation points and the fixed poles are chosen conveniently then the sequence of multipoint rational approximants converges geometrically to f in the chordal metric on compact subsets of$\bbfC\setminus I\$.The second author (G.L.L.) was supported by Dirección General de Enseñanza Superior under Grant PB 96-0120-C03-01 and by INTAS under Grant 93-0219 EXT.Publicad

Convergence and Asymptotic of Multi-Level Hermite-Padé Polynomials

Mención Internacional en el título de doctorPrograma de Doctorado en Ingeniería Matemática por la Universidad Carlos III de MadridPresidente: Francisco José Marcellán Español.- Secretario: Bernardo de la Calle Ysern.- Vocal: Arnoldus Bernardus Jacobus Kuijla

Multipoint Padé-type approximants. Exact rate of convergence

14 pages, no figures.-- MSC1991 codes: Primary 41A21, 41A25; Secondary 30E10, 42C05.MR#: MR1606915 (99i:41016)Zbl#: Zbl 0896.41010We study the rate with which sequences of interpolating rational functions, whose poles are partially fixed, approximate Markov-type analytic functions. Applications to interpolating quadratures are given.The authors were partially supported by Research Grant 93-277 RG/Maths/LA from the Third World Academy of Science.Publicad

Systems of Markov type functions: normality and convergence of Hermite-Padé approximants

This thesis deals with Hermite-Padé approximation of analytic and merophorphic functions. As such it is embeded in the theory of vector rational approximation of analytic functions which in turn is intimately connectd with the theory of multiple orthogonal polynomials. All the basic concepts and results used in this thesis involving complex analysis and measure theory may found in classical textbooks...........Programa Oficial de Doctorado en Ingeniería MatemáticaPresidente: Francisco José Marcellán Español; Vocal: Alexander Ivanovich Aptekarev; Secretario: Andrei Martínez Finkelshtei

On Multipoint Padé Approximants whose Poles Accumulate on Contours that Separate the Plane

In this note we consider asymptotics of the multipoint Padé approximants to Cauchy integrals of analytic non-vanishing densities defined on a Jordan arc connecting -1 and 1. We allow for the situation where the (symmetric) contour attracting the poles of the approximants does separate the plane

On the convergence of quadrature formulas connected with multipoint Padé-type approximants

29 pages, no figures.-- MSC2000 codes: 41A55, 41A21.MR#: MR1408352 (97e:41066)Zbl#: Zbl 0856.41027^aLet $I(F)= \int^1_{- 1} F(x)\omega(x) dx$, where $\omega$ is a complex valued integrable function. We consider quadrature formulas for $I(F)$ which are exact with respect to rational functions with prescribed poles contained in \overline{\bbfC}\backslash [- 1, 1]. Their rate of convergence is studied.The research by the first three authors (P.G.-V., M.J.P., R.O.) was partially supported by the HCM project ROLLS, under Contract CHRX-CT93-0416. Research by the fourth author (G.L.L.) was carried out while on a visit at Universidad de La Laguna. This visit was made possible by a travel grant from CDE-IMU.Publicad

Forms of the symmetry energy relevant to neutron stars

The symmetry energy is an invaluable tool for studying dense nuclearmatter. Unfortunately, its definition is somewhat implicit, and therefore, phenomenologicalmethods are necessary to describe experimental facts. This paper discusses the differences arising from the use of Taylor series expansion and Padé approximation to determine theoretically the symmetry energy and the possible consequences for neutron stars. For this purpose, a form of the nuclear matter equation of state that explicitly depends on the symmetry energy is used. The obtained results point out that the applied approximations lead to modifications of the equilibrium proton fractions and equation of state, especially in their high-density limit. However, this effect is small near the saturation density n0

On the convergence of quadrature formulas connected with multipoint Padé-type approximants

29 pages, no figures.-- MSC2000 codes: 41A55, 41A21.MR#: MR1408352 (97e:41066)Zbl#: Zbl 0856.41027^aLet $I(F)= \int^1_{- 1} F(x)\omega(x) dx$, where $\omega$ is a complex valued integrable function. We consider quadrature formulas for $I(F)$ which are exact with respect to rational functions with prescribed poles contained in \overline{\bbfC}\backslash [- 1, 1]. Their rate of convergence is studied.The research by the first three authors (P.G.-V., M.J.P., R.O.) was partially supported by the HCM project ROLLS, under Contract CHRX-CT93-0416. Research by the fourth author (G.L.L.) was carried out while on a visit at Universidad de La Laguna. This visit was made possible by a travel grant from CDE-IMU.Publicad