𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Rational Approximation with Locally Geometric Rates

✍ Scribed by A.L Levin; V.V Maimeskul; E.B Saff

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
425 KB
Volume
92
Category
Article
ISSN
0021-9045

No coin nor oath required. For personal study only.

✦ Synopsis

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 functions ``near best'' polynomials converging geometrically fast at every point of analyticity of the function exist. Here we construct rational approximants enjoying similar properties. We also show that our construction yields rates of convergence that are, in a certain sense, best possible.

πŸ“œ SIMILAR VOLUMES

Rational Approximation with Varying Weig
Rational Approximation with Varying Weights, II
✍ E.A Rakhmanov; E.B Saff; P.C Simeonov πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 275 KB

We consider two problems concerning uniform approximation by weighted rational functions [w n r n ] n=1 , where r n = p n Γ‚q 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

Multipoint Rational Approximants with Pr
Multipoint Rational Approximants with Preassigned Poles
✍ Francisco Cala Rodrı́guez; Guillermo LΓ³pez Lagomasino πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 136 KB

Let be a finite positive Borel measure whose support S is a compact Ε½ . Ε½ . Ε½ regular set contained in ‫.ޒ‬ For a function of Markov type z s H d x r z Λ†SΕ½ . . Ε½ . Ε½ . y x , z g ‫ރ‬ \_ S , we consider multipoint Pade-type approximants MPTAs , αΊƒhere some poles are preassigned and interpolation is ca

Geometric sensitivity analysis with loca
Geometric sensitivity analysis with local coordinate transformations
✍ Brockman, R. A. πŸ“‚ Article πŸ“… 1988 πŸ› Wiley (John Wiley & Sons) 🌐 English βš– 367 KB

The dimensionality of truss, beam, membrane and shell finite elements is often less than that of the global co-ordinate system, and element calculations must be performed in local co-ordinates. Design parameters which affect the nodal co-ordinates in such elements control both the element dimensions