On positive cubature rules on the simplex and isometric embeddings

Details On positive cubature rules on the simplex and isometric embeddings On positive cubature rules on the simplex and isometric embeddings

2011-08-17

arxiv.org/abs/1108.3385v1

Mathematics

Numerical Analysis

27 pages

Scientific paper

Positive cubature rules of degree 4 and 5 on the $d$-dimensional simplex are constructed and used to construct cubature rules of index 8 or degree 9 on the unit sphere. The latter ones lead to explicit isometric embedding among the classical Banach spaces. Among other things, our results include several explicit representations of $(x_1^2+...+ x_d^2)^t$ in terms of linear forms of degree $2t$ with rational coefficients for t=4 and 5.

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