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ACM monograph series
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 =
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg – Springer Journals
Published: Aug 28, 2008
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