𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Multipoint Rational Approximants with Preassigned Poles

✍ Scribed by Francisco Cala Rodrı́guez; Guillermo López Lagomasino

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
136 KB
Volume
256
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis

Let be a finite positive Borel measure whose support S is a compact Ž . Ž . Ž regular set contained in ‫.ޒ‬ For a function of Markov type z s H d x r z ˆSŽ .

. Ž . Ž . y x , z g ‫ރ‬ _ S , we consider multipoint Pade-type approximants MPTAs , ẃhere some poles are preassigned and interpolation is carried out along a table of Ž Ž .. points contained in ‫ރ‬ _ Co S which is symmetrical with respect to the real line. The main purpose of this paper is the study of the ''exact rate of convergence'' of the MPTAs to the function .

📜 SIMILAR VOLUMES

Convergence of Rational Interpolants wit
Convergence of Rational Interpolants with Preassigned Poles
✍ Amiran Ambroladze; Hans Wallin 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 336 KB

We study the following problem. Given a domain 0 containing infinity, is it possible to choose a sequence of polynomials Q n , n=1, 2, ..., where Q n has degree n, so that the following condition holds: if a function f is analytic in 0 and P n is the polynomial part of the Laurent expansion of Q n f

Approximation of analytic functions by r
Approximation of analytic functions by rational functions with prescribed poles
✍ Gaetano Fichera 📂 Article 📅 1970 🏛 John Wiley and Sons 🌐 English ⚖ 473 KB

From (1) it follows that y ( z ) has in zk a zero of order not less than vk . Since y ( z ) is holomorphic in the neighborhood of every point of %'K (including z = a), it follows from Hypothesis 6, that y ( z ) vanishes identically in VK. On the other hand, we have for large IzJ of 5. 1 We say tha

Approximation of Transfer Functions of I
Approximation of Transfer Functions of Infinite Dimensional Dynamical Systems by Rational Interpolants with Prescribed Poles
✍ Angel Ribalta Stanford; Guillermo López Lagomasino 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 171 KB

Rational interpolants with prescribed poles are used to approximate holomorphic functions on the closure of their region of analyticity under natural assumptions of their properties on the boundary. The transfer functions of some infinite dimensional dynamical systems of interest in applications sat

Rational Approximation with Locally Geom
Rational Approximation with Locally Geometric Rates
✍ A.L Levin; V.V Maimeskul; E.B Saff 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 425 KB

We investigate the rate of pointwise rational approximation of functions from two classes. The distinguishing feature of these classes is the essentially faster convergence of the best uniform rational approximants versus best uniform polynomial approximants. It is known that for piecewise analytic

Rational Approximation with Varying Weig
Rational Approximation with Varying Weights, II
✍ E.A Rakhmanov; E.B Saff; P.C Simeonov 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 275 KB

We consider two problems concerning uniform approximation by weighted rational functions [w n r n ] n=1 , where r n = p n Âq n has real coefficients, deg p n [:n] and deg q n [;n], for given :>0 and ; 0. For w(x) :=e x we show that on any interval [0, a] with a # (0, a^(:, ;)), every real-valued fun