General Results on the Convergence of Multipoint Hermite-Pade Approximants of Nikishin Systems
نویسندگان
چکیده
منابع مشابه
Sufficient Conditions for the Convergence of Multipoint Hermite-padé Approximants of Nikishin Systems
We consider simultaneous approximation of Nikishin systems of functions by means of rational vector functions which are constructed interpolating along a prescribed table of points. We give sufficient conditions for the uniform convergence of such approximants with a geometric rate.
متن کاملRate of Convergence of Generalized Hermite-padé Approximants of Nikishin Systems
We study the rate of convergence of interpolating simultaneous rational approximations with partially prescribed poles to so called Nikishin systems of functions. To this end, a vector equilibrium problem in the presence of a vector external field is solved which is used to describe the asymptotic behavior of the corresponding second type functions which appear. 1. Generalized Hermite-Padé appr...
متن کاملConvergence of Multipoint Padé-type Approximants
Let 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 C \ I and r(∞) = 0. We consider multipoint rational interpolants of the function f (z) = dµ(x) z − x + r(z), where some poles are fixed and others are left free. We show that if the interpolati...
متن کاملTwo-point Pade approximants
We present analytic estimates for the energy levels of N electrons (N = 2−5) in a two-dimensional parabolic quantum dot. A magnetic field is applied perpendicularly to the confinement plane. The relevant scaled energy is shown to be a smooth function of the parameter β=(effective Rydberg/effective dot energy)1/6. Two-point Pade approximants are obtained from the series expansions of the energy ...
متن کاملGeneralized Hermite-Padé approximation for Nikishin systems of three functions
Nikishin systems of three functions are considered. For such systems, the rate of convergence of simultaneous interpolating rational approximations with partially prescribed poles is studied. The solution is described in terms of the solution of a vector equilibrium problem in the presence of a vector external field.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Constructive Approximation
سال: 2006
ISSN: 0176-4276,1432-0940
DOI: 10.1007/s00365-006-0630-y