Summary
An extension of the Clenshaw-Curtis quadrature method is described for integrals involving absolutely integrable weight functions. The resulting quadrature rules turn out to be slightly lower in accuracy than the corresponding Gaussian rules. This, however, seems to be paid off by the use of preassigned nodes and by the applicability of Fast Fourier Transform techniques. Some specific formulae are derived explicitly and several numerical examples are given.
Zusammenfassung
Das Quadraturverfahren von Clenshaw und Curtis wird auf Integrale übertragen, die absolut integrierbare klassische Gewichtsfunktionen enthalten. Es stellt sich heraus, daß die entstehenden Quadraturformeln in der Genauigkeit den entsprechenden Gaußschen Formeln nur wenig nachstehen, jedoch wegen der vorgegebenen Stützstellen und wegen der Anwendbarkeit des Algorithmus von Cooley und Tukey numerische Vorteile besitzen. Einige Formeln werden zusammen mit numerischen Beispielen explizit angegeben.
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This work was supported by the Office of Naval Research under contract NR 044-37.
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Kussmaul, R. Clenshaw-Curtis quadrature with a weighting function. Computing 9, 159–164 (1972). https://doi.org/10.1007/BF02236965
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DOI: https://doi.org/10.1007/BF02236965