Partially symmetric cubature formulas for even degrees of exactness
SIAM Journal on Numerical Analysis
Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Monomial cubature rules since “Stroud”: a compilation
Journal of Computational and Applied Mathematics
Regular Article: Cubature Formulae and Polynomial Ideals
Advances in Applied Mathematics
Monomial cubature rules since “Stroud”: a compilation—part 2
Journal of Computational and Applied Mathematics - Numerical evaluation of integrals
An interactive tool to visualize common zeros of two-dimensional polynomials
Journal of Computational and Applied Mathematics - Numerical evaluation of integrals
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We use positivity and extension properties of moment matrices to prove that a 10-node (minimal) cubature rule of degree 6 for planar measure on the closed unit disk D cannot have all nodes in D. We construct examples showing that such rules may have as many as 9 points in D, and we provide similar examples for the triangle.