Abstract
Error bounds are derived for the Lagrange interpolation formula and for the k-th derivative of the residual term of this formula in terms of the Lipschitz constant of the n-th derivative for the case with (n+1) nodes and also for the case when the functions satisfy a special condition: ∃G ∃ℝ ∀x, y, z ∃ [a, b]: ¦ ϕ(x)(z−y) +Φ(y)(x−z)+Φ(z)(y−x)¦≤G¦(x−y)(y−z)(z−x)¦.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
I. S. Bakhvalov, N. P. Zhidkov, and G. M. Kobel'kov, Numerical Methods [in Russian], Moscow (1987).
B. P. Demidovich and I. A. Maron, Foundations of Computational Mathematics [in Russian], Moscow (1966).
V. I. Krylov, V. V. Bobkov, and P. I. Monastyrnyi, Computational Methods [in Russian], Vol. 1, Moscow (1976).
I. I. Lyashko, V. L. Makarov, and A. A. Skorobogat'ko, Computational Methods [in Russian], Kiev (1977).
A. F. Kalaida, “On error of numerical differentiation formulas,” Vychisl. Prikl. Mat., No. 54, 16–26 (1984).
Author information
Authors and Affiliations
Additional information
Translated from Vychislitel'naya i Prikladnaya Matematika, No. 73, pp. 27–32, 1992.
Rights and permissions
About this article
Cite this article
Golovach, G.P. Some more general bounds on the residual term of the Lagrange interpolation formula. J Math Sci 71, 2645–2649 (1994). https://doi.org/10.1007/BF02114038
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02114038