Abstract

The construction of a cubature formula requires the solution of a large system of nonlinear equations for determining the knots and weights. The number of equations and unknowns can be reduced by imposing some structure on the formula. We construct cubature formulae for circular symmetric regions, with knots on regular polygons. Due to our special structure, we obtain a reduction of the number of equations and unknowns and the systems of nonlinear equations can be solved automatically and quickly. In this paper an algorithm is described and used to construct cubature formulae and sequences of embedded cubature formulae.

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