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Perfectly Symmetric Two-Dimensional Integration Formulas with Minimal Numbers of Points

Philip Rabinowitz and Nira Richter
Mathematics of Computation
Vol. 23, No. 108 (Oct., 1969), pp. 765-779
DOI: 10.2307/2004962
Stable URL: http://www.jstor.org/stable/2004962
Page Count: 15
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Perfectly Symmetric Two-Dimensional Integration Formulas with Minimal Numbers of Points
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Abstract

Perfectly symmetric integration formula of degrees 9-15 with a minimal number of points are computed for the square, the circle and the entire plane with weight functions exp(- (x2 + y2)) and exp(- (x2 + y2)1/2). These rules were computed by solving a large system of nonlinear algebraic equations having a special structure. In most cases where the minimal formula has a point exterior to the region or where some of the weights are negative, `good' formulas, which consist only of interior points and have only positive weights, are given which contain more than the minimal number of points.

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