Abstract
A construction method for cubature formulae of an arbitrary degree ford-dimensional product-integrals,d≥2, will be presented. To get a high degree of exactness with a moderate number of nodes quadrature rules are blended in a suitable way. For product-integrals with Tschebycheff-weight-functions the corresponding cubature formulae are minimal or ‘minimal + 1’ in the cased=2. In higher dimensions the number of nodes of the constructed formulae is far beyond the number of nodes of other approaches known.
Zusammenfassung
Es wird eine Konstruktionsmethode für Kubaturformeln beliebigen Grades fürd-dimensionale Produktintegrale,d≥2, entwickelt. Um einen möglichst hohen Exaktheitsgrad mit einer möglichst geringen Knotenzahl zu erhalten, werden Quadraturformeln in geeigneter Weise gemischt. Für Produktintegrale mit Tschebycheff-Gewichten ergeben sich im Falld=2 minimale oder ‘minimale + 1’-Kubaturformeln und in höheren Dimensionen Formeln, deren Knotenzahl weit unter derjenigen von bisher bekannten Formeln liegt.
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Godzina, G. Blending methods for two classical integrals. Computing 54, 273–282 (1995). https://doi.org/10.1007/BF02253617
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DOI: https://doi.org/10.1007/BF02253617