Bounds-constrained polynomial approximation using the Bernstein basis

DOI10.1007/s00211-022-01311-1OpenAlexW3157902398WikidataQ114231012 ScholiaQ114231012MaRDI QIDQ2168063

Larry Allen, Robert C. Kirby

Publication date: 31 August 2022

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.11819

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Quadratic programming (90C20) Approximation by rational functions (41A20) Approximation with constraints (41A29) Algorithms for approximation of functions (65D15)

Uses Software

• HE-E1GODF
• CVXPY
• SCS
• GitHub

Cites Work

• Conic optimization via operator splitting and homogeneous self-dual embedding
• Fast simplicial quadrature-based finite element operators using Bernstein polynomials
• Fast inversion of the simplicial Bernstein mass matrix
• Subcell flux limiting for high-order Bernstein finite element discretizations of scalar hyperbolic conservation laws
• A projection algorithm on the set of polynomials with two bounds
• Best uniform polynomial approximation of some rational functions
• The best uniform polynomial approximation to class of the form \(\frac{1}{(a^2\pm x^2)}\)
• Best approximation and interpolation of \((1+(ax)^2)^{-1}\) and its transforms.
• Legendre-Bernstein basis transformations
• Polynomials with bounds and numerical approximation
• Construction of orthogonal bases for polynomials in Bernstein form on triangular and simplex domains
• Fast simplicial finite element algorithms using Bernstein polynomials
• The best approximation of some rational functions in uniform norm
• Monolithic convex limiting in discontinuous Galerkin discretizations of hyperbolic conservation laws
• CVXPY: A Python-Embedded Modeling Language for Convex Optimization
• Spline Functions on Triangulations
• Sums of even powers of real linear forms
• Polynomials that are positive on an interval
• Algorithms For Positive Polynomial Approximation
• Semidefinite Programming
• Structured Inversion of the Bernstein--Vandermonde Matrix
• Structured Inversion of the Bernstein Mass Matrix
• A Sum of Squares Approximation of Nonnegative Polynomials
• Best approximation in inner product spaces
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