Multivariate approximation by polynomial and generalized rational functions

DOI10.1080/02331934.2022.2044478zbMath1489.41019arXiv2101.11786OpenAlexW4214857571MaRDI QIDQ5077169

R. Díaz Millán, Nadezda Sukhorukova, Julien Ugon, V. Peiris

Publication date: 18 May 2022

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.11786

zbMATH Keywords

quasiconvex functionsbisection methodChebyshev approximationgeneralized rational approximation

Mathematics Subject Classification ID

Applications of mathematical programming (90C90) Minimax problems in mathematical programming (90C47) Nonconvex programming, global optimization (90C26) Approximation by rational functions (41A20) Multidimensional problems (41A63) Algorithms for approximation of functions (65D15)

Related Items (3)

Solarity and proximinality in generalized rational approximation in spaces \(C(Q)\) and \(L^p\) ⋮ RATIONAL AND GENERALISED RATIONAL CHEBYSHEV APPROXIMATION PROBLEMS AND THEIR APPLICATIONS ⋮ Existence, uniqueness, and stability of best and near-best approximations

Uses Software

• AAA

Cites Work

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• Subgradient projection algorithms and approximate solutions of convex feasibility problems
• Uniform approximation by the highest defect continuous polynomial splines: Necessary and sufficient optimality conditions and their generalisations
• Bivariate segment approximation and free knot splines: Research Problems 96-4
• Chebyshev multivariate polynomial approximation: alternance interpretation
• Finite alternation theorems and a constructive approach to piecewise polynomial approximation in Chebyshev norm
• Chebyshev approximation by a rational expression for functions of many variables
• Functions whose best rational Chebyshev approximation are polynomials
• Rational Chebyshev approximation by Remes' algorithms
• Polynomials of best uniform approximation to certain rational functions
• Generalised rational approximation and its application to improve deep learning classifiers
• Dykstras algorithm with bregman projections: A convergence proof
• On the finite termination of the Douglas-Rachford method for the convex feasibility problem
• Some modified relaxed alternating projection methods for solving the two-sets convex feasibility problem
• Algorithms for Chebyshev Approximations Using the Ratio of Linear Forms
• Algorithms for Piecewise Polynomials and Splines with Free Knots
• Chebyshev Approximation by Spline Functions with Free Knots
• On the convergence of general projection methods for solving convex feasibility problems with applications to the inverse problem of image recovery
• An Algorithm for Real and Complex Rational Minimax Approximation
• Characterisation theorem for best polynomial spline approximation with free knots
• Generalized Rational Approximation
• Tchebycheff Approximation in Several Variables
• Uniform Approximation by Chebyshev Spline Functions. II: Free Knots
• The AAA Algorithm for Rational Approximation

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