Optimal stability of the Lagrange formula and conditioning of the Newton formula

DOI10.1016/j.jat.2017.07.005zbMath1407.41002OpenAlexW2736010211MaRDI QIDQ1711823

Y. Khiar, J. M. Carnicer, Juan Manuel Peña

Publication date: 18 January 2019

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

Full work available at URL: http://zaguan.unizar.es/record/78093

zbMATH Keywords

Lagrange interpolation formulaNewton interpolation formulaSkeel condition numberLeja order

Mathematics Subject Classification ID

Numerical interpolation (65D05) Interpolation in approximation theory (41A05) Approximation by polynomials (41A10)

Related Items (16)

Inverse central ordering for the Newton interpolation formula ⋮ Conditioning of Fourier sums on a quadratic curve ⋮ An hp‐adaptive multi‐element stochastic collocation method for surrogate modeling with information re‐use ⋮ On the condition number of Newton interpolation: Chebyshev points and monotonically ordering ⋮ A novel multivariate spectral local quasilinearization method (MV-SLQLM) for modelling flow, moisture, heat, and solute transport in soil ⋮ On the stability of the representation of finite rank operators ⋮ Generalized Standard Triples for Algebraic Linearizations of Matrix Polynomials ⋮ On the conditioning of the Newton formula for Lagrange interpolation ⋮ Central orderings for the Newton interpolation formula ⋮ Stability properties of disk polynomials ⋮ Differentiation matrices for univariate polynomials ⋮ The Runge Example for Interpolation and Wilkinson's Examples for Rootfinding ⋮ Conditioning of polynomial Fourier sums ⋮ On the numerical stability of Newton's formula for Lagrange interpolation ⋮ Optimal interval length for the collocation of the Newton interpolation basis ⋮ Newton interpolation using \(\Re \)-Leja sequences

Uses Software

• mctoolbox

Cites Work

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• B-splines and optimal stability
• Barycentric Lagrange Interpolation
• The numerical stability of barycentric Lagrange interpolation
• On the optimal stability of the Bernstein basis
• Accuracy and Stability of Numerical Algorithms

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