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The determination of nodes and weights in wilf quadrature formulas

The determination of nodes and weights in wilf quadrature formulas The Determination of Nodes and Weights in WILF Quadrature Formulas By H. ENGELS and U. ECKHARDT Dedicated to Prof. Dr. L: COLLATZ Oil the occasion of his 65 m birthday, 6 m July 1975 Summary. Using a new characterization of WILF quadrature formulas due to ENGELS, nodes, weights, and error-constants of formulas of this type are computed. All formulas are based upon the interval [--1; 1]. The formulas are listed for N---- 2, 8, 32 with 25 significant digits. The computing process is described. Applications to some model problems in comparison with Gaussian quadrature show very good results. Zusammeniassung. Unter Verwendung einer neuen Charakterisierung Wilfscher Quadraturformeln yon EI~GELS werden Stiitzstellen, Ge- wichte und Fehlerkonstanten yon Quadraturformeln dieses Typs be- rechnet. Alle Formeln sind auf das Intervall [-- 1 ; 1] bezogen. Die For- mein sind fiir N = 2, 8, 32 mit 25 signifikanten Dezimalen angegeben. Das Berechnungsverfahren wird beschrieben. Anwendungsbeispiele zeigen im Vergleich mit der Gaui3-Quadratur sehr gute Ergebnisse. 1. Survey In [7] H. S. WILF presented a new quadrature procedure by the requirement, that oo 1 0.1) Q.:= Z d --Z v=O 0 i=1 should be minimal. Here xi, i-----l(1)n, are the nodes, and A,, i = http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Springer Journals

The determination of nodes and weights in wilf quadrature formulas

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References (8)

Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Mathematics, general; Algebra; Differential Geometry; Number Theory; Topology; Geometry
ISSN
0025-5858
eISSN
1865-8784
DOI
10.1007/BF02941288
Publisher site
See Article on Publisher Site

Abstract

The Determination of Nodes and Weights in WILF Quadrature Formulas By H. ENGELS and U. ECKHARDT Dedicated to Prof. Dr. L: COLLATZ Oil the occasion of his 65 m birthday, 6 m July 1975 Summary. Using a new characterization of WILF quadrature formulas due to ENGELS, nodes, weights, and error-constants of formulas of this type are computed. All formulas are based upon the interval [--1; 1]. The formulas are listed for N---- 2, 8, 32 with 25 significant digits. The computing process is described. Applications to some model problems in comparison with Gaussian quadrature show very good results. Zusammeniassung. Unter Verwendung einer neuen Charakterisierung Wilfscher Quadraturformeln yon EI~GELS werden Stiitzstellen, Ge- wichte und Fehlerkonstanten yon Quadraturformeln dieses Typs be- rechnet. Alle Formeln sind auf das Intervall [-- 1 ; 1] bezogen. Die For- mein sind fiir N = 2, 8, 32 mit 25 signifikanten Dezimalen angegeben. Das Berechnungsverfahren wird beschrieben. Anwendungsbeispiele zeigen im Vergleich mit der Gaui3-Quadratur sehr gute Ergebnisse. 1. Survey In [7] H. S. WILF presented a new quadrature procedure by the requirement, that oo 1 0.1) Q.:= Z d --Z v=O 0 i=1 should be minimal. Here xi, i-----l(1)n, are the nodes, and A,, i =

Journal

Abhandlungen aus dem Mathematischen Seminar der Universität HamburgSpringer Journals

Published: Aug 28, 2008

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