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Accelerated polynomial approximation of finite order entire functions by growth reduction

Identifieur interne : 001603 ( PascalFrancis/Curation ); précédent : 001602; suivant : 001604

Accelerated polynomial approximation of finite order entire functions by growth reduction

Auteurs : J. Müller [Allemagne]

Source :

Mathematics of computation [ 0025-5718 ] ; 1997.

RBID : Pascal:97-0302699

Descripteurs français

Pascal (Inist)
- Méthode numérique, Accélération convergence, Approximation polynomiale, Fonction entière, Fonction variable complexe, Fonction Bessel, Estimation erreur.

English descriptors

KwdEn :
- Bessel function, Complex variable function, Convergence acceleration, Entire function, Error estimation, Numerical methods, Polynomial approximation.

Abstract

Let f be an entire function of positive order and finite type. The subject of this note is the convergence acceleration of polynomial approximants of f by incorporating information about the growth of f(z) for z → ∞. We consider "near polynomial approximation" on a compact plane set K, which should be thought of as a circle or a real interval. Our aim is to find sequences (f_n)_n of functions which are the product of a polynomial of degree < n and an "easy computable" second factor and such that (f_n)_n converges essentially faster to f on K than the sequence (P_n^*)_n of best approximating polynomials of degree ≤ n. The resulting method, which we call Reduced Growth method (RG-method) is introduced in Section 2. In Section 5, numerical examples of the RG-method applied to the complex error function and to Bessel functions are given.

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A05				`@2 66`
A06				`@2 218`
A08	`01`	`1`	`ENG`	`@1 Accelerated polynomial approximation of finite order entire functions by growth reduction`
A11	`01`	`1`		`@1 MÜLLER (J.)`
A14	`01`			`@1 Fachbereich IV-Mathematik, Universität Trier @2 54286 Trier @3 DEU @Z 1 aut.`
A20				`@1 743-761`
A21				`@1 1997`
A23	`01`			`@0 ENG`
A43	`01`			`@1 INIST @2 5227 @5 354000065245410150`
A44				`@0 0000 @1 © 1997 INIST-CNRS. All rights reserved.`
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A61				`@0 A`
A64	`01`	`1`		`@0 Mathematics of computation`
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C01	`01`		`ENG`	@0 Let f be an entire function of positive order and finite type. The subject of this note is the convergence acceleration of polynomial approximants of f by incorporating information about the growth of f(z) for z → ∞. We consider "near polynomial approximation" on a compact plane set K, which should be thought of as a circle or a real interval. Our aim is to find sequences (f_n)_n of functions which are the product of a polynomial of degree < n and an "easy computable" second factor and such that (f_n)_n converges essentially faster to f on K than the sequence (P_n^*)_n of best approximating polynomials of degree ≤ n. The resulting method, which we call Reduced Growth method (RG-method) is introduced in Section 2. In Section 5, numerical examples of the RG-method applied to the complex error function and to Bessel functions are given.
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C02	`02`	`X`		`@0 001A02I01D`
C03	`01`	`1`	`FRE`	`@0 Méthode numérique @3 P @5 01`
C03	`01`	`1`	`ENG`	`@0 Numerical methods @3 P @5 01`
C03	`02`	`X`	`FRE`	`@0 Accélération convergence @5 51`
C03	`02`	`X`	`ENG`	`@0 Convergence acceleration @5 51`
C03	`02`	`X`	`SPA`	`@0 Aceleración convergencia @5 51`
C03	`03`	`X`	`FRE`	`@0 Approximation polynomiale @5 52`
C03	`03`	`X`	`ENG`	`@0 Polynomial approximation @5 52`
C03	`03`	`X`	`SPA`	`@0 Aproximación polinomial @5 52`
C03	`04`	`X`	`FRE`	`@0 Fonction entière @5 53`
C03	`04`	`X`	`ENG`	`@0 Entire function @5 53`
C03	`04`	`X`	`SPA`	`@0 Función entera @5 53`
C03	`05`	`X`	`FRE`	`@0 Fonction variable complexe @5 54`
C03	`05`	`X`	`ENG`	`@0 Complex variable function @5 54`
C03	`05`	`X`	`SPA`	`@0 Función variable compleja @5 54`
C03	`06`	`X`	`FRE`	`@0 Fonction Bessel @5 55`
C03	`06`	`X`	`ENG`	`@0 Bessel function @5 55`
C03	`06`	`X`	`SPA`	`@0 Función Bessel @5 55`
C03	`07`	`X`	`FRE`	`@0 Estimation erreur @5 56`
C03	`07`	`X`	`ENG`	`@0 Error estimation @5 56`
C03	`07`	`X`	`SPA`	`@0 Estimación error @5 56`
N21				`@1 174`

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<front><div type="abstract" xml:lang="en">Let f be an entire function of positive order and finite type. The subject of this note is the convergence acceleration of polynomial approximants of f by incorporating information about the growth of f(z) for z → ∞. We consider "near polynomial approximation" on a compact plane set K, which should be thought of as a circle or a real interval. Our aim is to find sequences (f<sub>n</sub>
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Accelerated polynomial approximation of finite order entire functions by growth reduction

Accelerated polynomial approximation of finite order entire functions by growth reduction

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Descripteurs français

English descriptors

Abstract

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