Treating the Gibbs phenomenon in barycentric rational interpolation and approximation via the S-Gibbs algorithm

DOI10.1016/j.aml.2019.106196zbMath1440.41004OpenAlexW2998494164MaRDI QIDQ2184976

Jean-Paul Berrut, Giacomo Elefante, F. Marchetti, Stefano De Marchi

Publication date: 4 June 2020

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/11577/3323880

zbMATH Keywords

Gibbs phenomenonbarycentric rational interpolationAAA algorithmfake nodesFloater-Hormann interpolant

Mathematics Subject Classification ID

Numerical smoothing, curve fitting (65D10) Approximation by rational functions (41A20) Numerical interpolation (65D05) Interpolation in approximation theory (41A05) Algorithms for approximation of functions (65D15)

Related Items (11)

Polynomial mapped bases: theory and applications ⋮ Padua points and fake nodes for polynomial approximation: old, new and open problems ⋮ Multivariate approximation at fake nodes ⋮ Adaptive rational interpolation for cell-average ⋮ On Kosloff Tal-Ezer least-squares quadrature formulas ⋮ More properties of \((\beta,\gamma)\)-Chebyshev functions and points ⋮ On \((\beta,\gamma)\)-Chebyshev functions and points of the interval ⋮ Generalizations of the constrained mock-Chebyshev least squares in two variables: tensor product vs total degree polynomial interpolation ⋮ Stable discontinuous mapped bases: the Gibbs-Runge-avoiding stable polynomial approximation (GRASPA) method ⋮ A linear barycentric rational interpolant on starlike domains ⋮ Mapped polynomials and discontinuous kernels for Runge and Gibbs phenomena

Uses Software

• FakeNodes
• AAA

Cites Work

• Unnamed Item
• Bounding the Lebesgue constant for Berrut's rational interpolant at general nodes
• Barycentric rational collocation methods for a class of nonlinear parabolic partial differential equations
• Rational functions for guaranteed and experimentally well-conditioned global interpolation
• Some results on linear rational trigonometric interpolation
• The linear barycentric rational method for a class of delay Volterra integro-differential equations
• Representation of conformal maps by rational functions
• Polynomial interpolation via mapped bases without resampling
• A periodic map for linear barycentric rational trigonometric interpolation
• Barycentric rational interpolation with no poles and high rates of approximation
• Barycentric Interpolation
• On the Gibbs Phenomenon and Its Resolution
• Rational Minimax Approximation via Adaptive Barycentric Representations
• Barycentric Lagrange Interpolation
• The numerical stability of barycentric Lagrange interpolation
• The Conditioning of a Linear Barycentric Rational Interpolant
• The AAA Algorithm for Rational Approximation
• The linear rational collocation method

This page was built for publication: Treating the Gibbs phenomenon in barycentric rational interpolation and approximation via the S-Gibbs algorithm