Bounding the Lebesgue constant for Berrut's rational interpolant at general nodes

DOI10.1016/j.jat.2013.01.004zbMath1281.41001OpenAlexW1985922315MaRDI QIDQ387252

Stefano De Marchi, Jean Sidon, Kai Hormann, L. P. Bos

Publication date: 20 December 2013

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2013.01.004

zbMATH Keywords

Lebesgue constantbarycentric rational approximation

Mathematics Subject Classification ID

Interpolation in approximation theory (41A05)

Related Items (15)

The Conditioning of a Linear Barycentric Rational Interpolant ⋮ Convergence rates of derivatives of Floater-Hormann interpolants for well-spaced nodes ⋮ Rational interpolation operator with finite Lebesgue constant ⋮ Treating the Gibbs phenomenon in barycentric rational interpolation and approximation via the S-Gibbs algorithm ⋮ Barycentric Interpolation ⋮ Linear Barycentric Rational Interpolation with Guaranteed Degree of Exactness ⋮ Optimal asymptotic Lebesgue constant of Berrut's rational interpolation operator for equidistant nodes ⋮ Local and global error estimates for Berrut's rational interpolant at well-spaced nodes ⋮ The effects of rounding errors in the nodes on barycentric interpolation ⋮ Lebesgue constant using sinc points ⋮ Recent advances in linear barycentric rational interpolation ⋮ Bounding the Lebesgue constant for a barycentric rational trigonometric interpolant at periodic well-spaced nodes ⋮ A convergent family of bivariate Floater-Hormann rational interpolants ⋮ Mapped polynomials and discontinuous kernels for Runge and Gibbs phenomena ⋮ On the numerical stability of linear barycentric rational interpolation

Cites Work

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• On the Lebesgue constant of barycentric rational interpolation at equidistant nodes
• On the Lebesgue constant of Berrut's rational interpolant at equidistant nodes
• Rational functions for guaranteed and experimentally well-conditioned global interpolation
• Lebesgue constant minimizing linear rational interpolation of continuous functions over the interval
• Weighted interpolation for equidistant nodes
• Barycentric rational interpolation with no poles and high rates of approximation
• A Rational Interpolation Scheme with Superpolynomial Rate of Convergence

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