Titlebook: Numerical Integration; Recent Developments, Patrick Keast,Graeme Fairweather Book 1987 D. Reidel Publishing Company, Dordrecht, Holland 198

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Construction of Sequences of Embedded Cubature Formulae for Circular Symmetric Planar Regionsr 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 nonlinea

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Fully Symmetric Integration Rules for the Unit Four-Cubelips (1967), Stenger (1971), Keast (1979), Genz and Malik (1980, 1983). In two and three dimensions, there also exist several rules of different degrees and over different regions. The only rules for the 4-cube we have been able to find are one degree 7 rule by Stroud (1967) and one degree 5 rule by

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On the Construction of Cubature Formulae with Few Nodes Using Groebner Basesdes. The formula exists if and only if F is an H-basis and some well-defined orthogonality conditions hold. Groebner bases and especially Buchberger’s algorithm for their computation allow an effective calculation of H-bases and easy proofs and generalizations of known methods based on H-bases. Groe

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