Error formulas for divided difference expansions and numerical differentiation

DOI10.1016/S0021-9045(03)00025-XzbMath1016.41016OpenAlexW2001407682MaRDI QIDQ1810589

Michael S. Floater

Publication date: 9 June 2003

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

Full work available at URL: https://doi.org/10.1016/s0021-9045(03)00025-x

zbMATH Keywords

Lagrange interpolationnumerical differentiationboundary-value problemsdivided differencesoptimal error boundsremaindersHowell and Shadrin's error bound

Mathematics Subject Classification ID

Remainders in approximation formulas (41A80) Proceedings, conferences, collections, etc. pertaining to approximations and expansions (41-06)

Related Items (9)

Error bounds in divided difference expansions. A probabilistic perspective ⋮ A conditional optimal upper bound for the argument of the Riemann zeta function on the critical line ⋮ Estimates for functionals with a known finite set of moments in terms of high order moduli of continuity in spaces of functions defined on a segment ⋮ On the divided differences of the remainder in polynomial interpolation ⋮ The Landau-Kolmogorov inequality revisited ⋮ Wavelet-based filters for accurate computation of derivatives ⋮ Approximation by \(B\)-spline convolution operators. A probabilistic approach ⋮ A divided difference expansion of a divided difference ⋮ Functional equations stemming from numerical analysis

Cites Work

• Derivative error bounds for Lagrange interpolation: An extension of Cauchy's bound for the error of Lagrange interpolation
• Error bounds for Lagrange interpolation
• Supra-Convergent Schemes on Irregular Grids
• A divided difference formula for the error in Hermite interpolation
• The Construction of Finite Difference Approximations to Ordinary Differential Equations
• Minimising Truncation Error in Finite Difference Approximations to Ordinary Differential Equations
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