On optimal polynomial meshes

DOI10.1016/j.jat.2011.03.007zbMath1229.65049OpenAlexW2041865361MaRDI QIDQ719352

András Kroó

Publication date: 10 October 2011

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2011.03.007

zbMATH Keywords

numerical examplesmultivariate polynomialsconvex polytopesadmissible optimal meshesconvex and star like setsgraph domainsnorming setspolynomial graphs

Mathematics Subject Classification ID

Related Items (26)

𝐿^{𝑝}-Bernstein inequalities on 𝐶²-domains and applications to discretization ⋮ Optimal polynomial admissible meshes on some classes of compact subsets of \(\mathbb{R}^d\) ⋮ Polynomial fitting and interpolation on circular sections ⋮ Multivariate ``needle polynomials with application to norming sets and cubature formulas ⋮ On discretizing uniform norms of exponential sums ⋮ Suboptimal Polynomial Meshes on Planar Lipschitz Domains ⋮ Marcinkiewicz-Zygmund type results in multivariate domains ⋮ On the existence of optimal meshes in every convex domain on the plane ⋮ Polynomial approximation and cubature at approximate Fekete and Leja points of the cylinder ⋮ An overdetermined B-spline collocation method for Poisson problems on complex domains ⋮ Pluripotential numerics ⋮ Polynomial approximation and quadrature on geographic rectangles ⋮ Bernstein type inequalities on star-like domains in $${\mathbb{R }}^d$$ with application to norming sets ⋮ Monotone trigonometric approximation ⋮ On generalized least power approximation ⋮ A note on total degree polynomial optimization by Chebyshev grids ⋮ Nearly optimal meshes in subanalytic sets ⋮ Geometric computation of Christoffel functions on planar convex domains ⋮ Subperiodic Dubiner distance, norming meshes and trigonometric polynomial optimization ⋮ Laplace Beltrami operator in the Baran metric and pluripotential equilibrium measure: the ball, the simplex, and the sphere ⋮ Tchakaloff polynomial meshes ⋮ Small perturbations of polynomial meshes ⋮ Near G-optimal Tchakaloff designs ⋮ Markov inequalities, Dubiner distance, norming meshes and polynomial optimization on convex bodies ⋮ Randomized weakly admissible meshes ⋮ Near-optimal polynomial interpolation on spherical triangles

Cites Work

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• Uniform approximation by discrete least squares polynomials
• On the approximation of convex bodies by convex algebraic level surfaces
• On Bernstein and Markov-type inequalities for multivariate polynomials on convex bodies
• Markov-type inequalities for surface gradients of multivariate polynomials
• A Markov inequality in several dimensions
• Markov-Bernstein type inequalities for multivariate polynomials on sets with cusps
• Weakly Admissible Meshes and Discrete Extremal Sets
• Geometric weakly admissible meshes, discrete least squares approximations and approximate Fekete points
• Low cardinality admissible meshes on quadrangles, triangles and disks
• Error estimates for scattered data interpolation on spheres

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