منابع مشابه
Optimal polynomial meshes and Caratheodory-Tchakaloff submeshes on the sphere
Using the notion of Dubiner distance, we give an elementary proof of the fact that good covering point configurations on the 2-sphere are optimal polynomial meshes. From these we extract CaratheodoryTchakaloff (CATCH) submeshes for compressed Least Squares fitting. 2010 AMS subject classification: 41A10, 65D32.
متن کاملOn optimal polynomial meshes
Let P d n be the the space of real algebraic polynomials of d variables and degree at most n, K ⊂ R a compact set, ||p||K := supx∈K |p(x)| the usual supremum norm on K, card(Y ) the cardinality of a finite set Y . A family of sets Y = {Yn ⊂ K, n ∈ N} is called an admissible mesh in K if there exists a constant c1 > 0 depending only on K such that ||p||K ≤ c1||p||Yn , p ∈ P d n , n ∈ N, where th...
متن کاملSmall perturbations of polynomial meshes
We show that the property of being a (weakly) admissible mesh for multivariate polynomials is preserved by small perturbations on real and complex Markov compacts. Applications are given to smooth transformations of polynomial meshes and to polynomial interpolation. 2000 AMS subject classification: 30E10, 41A10, 41A63, 65D05.
متن کاملPolynomial Meshes: Computation and Approximation
We present the software package WAM, written in Matlab, that generates Weakly Admissible Meshes and Discrete Extremal Sets of Fekete and Leja type, for 2d and 3d polynomial least squares and interpolation on compact sets with various geometries. Possible applications range from data fitting to high-order methods for PDEs.
متن کاملCaratheodory-Tchakaloff Subsampling
We present a brief survey on the compression of discrete measures by Caratheodory-Tchakaloff Subsampling, its implementation by Linear or Quadratic Programming and the application to multivariate polynomial Least Squares. We also give an algorithm that computes the corresponding CaratheodoryTchakaloff (CATCH) points and weights for polynomial spaces on compact sets and manifolds in 2D and 3D. 2...
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ژورنال
عنوان ژورنال: Annales Polonici Mathematici
سال: 2019
ISSN: 0066-2216,1730-6272
DOI: 10.4064/ap181031-26-3