A definiteness theory for cubature formulae of order two

DOI10.1007/s00365-005-0619-4zbMath1101.41030OpenAlexW1981885803MaRDI QIDQ851115

Otheman Nouisser, Allal Guessab, Gerhard Schmeisser

Publication date: 17 November 2006

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00365-005-0619-4

Mathematics Subject Classification ID

Partial orders, general (06A06) Inequalities and extremum problems involving convexity in convex geometry (52A40) Multidimensional problems (41A63) Inequalities for sums, series and integrals (26D15) Approximate quadratures (41A55) Convexity of real functions of several variables, generalizations (26B25) Numerical integration (65D30) Remainders in approximation formulas (41A80) Best constants in approximation theory (41A44)

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Approximations of differentiable convex functions on arbitrary convex polytopes ⋮ On approximation of linear functionals over convex functions: construction techniques and new directions ⋮ On the approximation of strongly convex functions by an upper or lower operator ⋮ Construction of positive definite cubature formulae and approximation of functions via Voronoi tessellations ⋮ A multivariate extension of an inequality of Brenner-Alzer ⋮ Best Constants for Weighted Poincaré–Type Inequalities ⋮ New cubature formulas and Hermite-Hadamard type inequalities using integrals over some hyperplanes in the \(d\)-dimensional hyper-rectangle ⋮ Generalized Barycentric Coordinates and Sharp Strongly Negative Definite Multidimensional Numerical Integration ⋮ Negative definite cubature formulae, extremality and Delaunay triangulation ⋮ A characterization for the validity of the Hermite-Hadamard inequality on a simplex

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