Fast and Stable Rational Interpolation in Roots of Unity and Chebyshev Points

DOI10.1137/100797291zbMath1252.41005OpenAlexW1975959460MaRDI QIDQ2903057

Ricardo Pachón, Pedro Gonnet, Joris Van Deun

Publication date: 23 August 2012

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/fb409596455173afda55ae5f3af0a7974aa5353c

zbMATH Keywords

rational interpolationdiscrete orthogonal polynomialsbarycentric interpolation formula

Mathematics Subject Classification ID

Approximation by rational functions (41A20) Interpolation in approximation theory (41A05)

Related Items (11)

Bandwidth truncation for Chebyshev polynomial and ultraspherical/Chebyshev Galerkin discretizations of differential equations: restrictions and two improvements ⋮ Rotation invariant patterns for a nonlinear Laplace-Beltrami equation: a Taylor-Chebyshev series approach ⋮ Stable polefinding and rational least-squares fitting via eigenvalues ⋮ Chebyshev approximation of multivariable functions by a constrained rational expression ⋮ Orthogonal polynomials on planar cubic curves ⋮ Fast barycentric rational interpolations for complex functions with some singularities ⋮ Practical algorithms for multivariate rational approximation ⋮ Rigorous numerics for ODEs using Chebyshev series and domain decomposition ⋮ Vandermonde with Arnoldi ⋮ Computing Eigenvalues of Real Symmetric Matrices with Rational Filters in Real Arithmetic ⋮ Alternation points, weights and orthogonal polynomials

Uses Software

• Algorithm 413
• Chebfun

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