Abstract
The weights and nodes of a symmetric cubature formula are determined by solving a system of nonlinear equations. The number of equations and their structure are investigated for symmetric cubature formulas for the square and the triangle. A new cubature formula of degree 7 with 12 nodes is given for the triangle.
Zusammenfassung
Die Gewichte und Knoten einer symmetrischen Kubaturformel werden durch Lösung eines nichtlinearen Gleichungsystems bestimmt. die Anzahl der Gleichungen und ihre Struktur werden für symmetrische Kubaturformeln für das Quadrat und das Dreieck untersucht. Eine neue Kubaturformel vom Grad 7 mit 12 Knoten wird für das Dreieck angegeben.
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Gatermann, K. The construction of symmetric cubature formulas for the square and the triangle. Computing 40, 229–240 (1988). https://doi.org/10.1007/BF02251251
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DOI: https://doi.org/10.1007/BF02251251