Abstract
For integrals with convex domains of integration we consider cubature formulae of degree r, r∈{2, 3}, with only positive weights and all nodes inside the domain. We show, that the minimal number of nodes for such formulae varies from 3 to at least 5 (for r=2) and from 3 to at least 9 (for r=3) in dependence of the shape of the domain.
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Möller, H.M. (1982). Gaussian Cubature Formulae of Degree 2 and 3. In: Hämmerlin, G. (eds) Numerical Integration. ISNM 57: International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 57. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6308-7_17
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DOI: https://doi.org/10.1007/978-3-0348-6308-7_17
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-6309-4
Online ISBN: 978-3-0348-6308-7
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