Approximations of differentiable convex functions on arbitrary convex polytopes

DOI10.1016/j.amc.2014.04.075zbMath1334.65037OpenAlexW1987755003MaRDI QIDQ279182

Allal Guessab

Publication date: 27 April 2016

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2014.04.075

zbMATH Keywords

convex functionsDelaunay triangulationbarycentric coordinatesfunction approximationbarycentric approximationupper approximation operator

Mathematics Subject Classification ID

Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Algorithms for approximation of functions (65D15) Convexity of real functions of several variables, generalizations (26B25) Approximation by arbitrary linear expressions (41A45)

Related Items (14)

Symmetrization procedures and convexity in centrally symmetric 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 ⋮ New stochastic fractional integral and related inequalities of Jensen-Mercer and Hermite-Hadamard-Mercer type for convex stochastic processes ⋮ A unified enrichment approach of the standard three-node triangular element ⋮ Enrichment strategies for the simplicial linear finite elements ⋮ 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 ⋮ A multivariate version of Hammer's inequality and its consequences in numerical integration ⋮ Numerical integration using integrals over hyperplane sections of simplices in a triangulation of a polytope ⋮ On a generalization of an approximation operator defined by A. Guessab ⋮ On new general versions of Hermite-Hadamard type integral inequalities via fractional integral operators with Mittag-Leffler kernel ⋮ A characterization for the validity of the Hermite-Hadamard inequality on a simplex ⋮ Sharp multidimensional numerical integration for strongly convex functions on convex polytopes

Cites Work

• A multivariate extension of an inequality of Brenner-Alzer
• Construction of positive definite cubature formulae and approximation of functions via Voronoi tessellations
• A definiteness theory for cubature formulae of order two
• Enhancement of the algebraic precision of a linear operator and consequences under positivity
• Convexity preserving interpolation
• Solution methodologies for the smallest enclosing circle problem
• Negative definite cubature formulae, extremality and Delaunay triangulation
• Mean value coordinates
• Continuity and convexity of projections and barycentric coordinates in convex polyhedra
• Multivariate approximation by a combination of modified Taylor polynomials
• Convexity results and sharp error estimates in approximate multivariate integration
• Coordination of groups of mobile autonomous agents using nearest neighbor rules
• Stability analysis of M-dimensional asynchronous swarms with a fixed communication topology
• The Minimum Covering Sphere Problem
• Sharp Error Estimates for Interpolatory Approximation on Convex Polytopes
• Unnamed Item
• Unnamed Item

This page was built for publication: Approximations of differentiable convex functions on arbitrary convex polytopes