Derivative error bounds for Lagrange interpolation: An extension of Cauchy's bound for the error of Lagrange interpolation

Howell, Gary W.

doi:10.1016/0021-9045(91)90015-3

Cited by 24 publications

(6 citation statements)

References 4 publications

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“…n,l (f ; x) which depends on the regularity of f (•). Our results extend results presented in [4], [5], [3], and [6] for regular functions f (•) ∈ AC n+1,∞ (I).…”

supporting

confidence: 89%

On Optimal Derivative Error Bounds for Lagrange Interpolation

Dubeau¹

2015

Int. J. of Pure and Appl. Math.

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“…n,l (f ; x) which depends on the regularity of f (•). Our results extend results presented in [4], [5], [3], and [6] for regular functions f (•) ∈ AC n+1,∞ (I).…”

supporting

confidence: 89%

On Optimal Derivative Error Bounds for Lagrange Interpolation

Dubeau¹

2015

Int. J. of Pure and Appl. Math.

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“…For α = n, this result was established earlier by Howell in [30]; another proof can be found in [31]. for all α ∈ [ 0 : n].…”

Section: C(e)supporting

confidence: 58%

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

Vinogradov

Zhuk

2014

St. Petersburg Math. J.

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A new technique is developed for estimating functionals in terms of the quantities mentioned in the title. The constants in estimates are indicated explicitly. As examples, Jackson type inequalities for approximations by polynomials and splines can be mentioned, along with estimates of error terms for interpolation formulas and for formulas of numerical differentiation and integration. One of results can be stated as follows. Let E be a segment, |E| its length, E n−1 the best uniform approximation by polynomials of degree at most n−1, and ω 2m the uniform modulus of continuity of order 2m. Let K r = 4 2010 Mathematics Subject Classification. Primary 41A15, 41A17, 41A35.

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“…The proof can easily be adapted from the error bound for the Lagrange interpolation, see Theorem 3 in [11].…”

Section: Accuracy Of the Spectral Difference Sbp Operatorsmentioning

confidence: 99%

A conservative and energy stable discontinuous spectral element method for the shifted wave equation in second order form

Duru¹,

Wang²,

Wiratama³

2021

Preprint

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In this paper, we develop a provably energy stable and conservative discontinuous spectral element method for the shifted wave equation in second order form. The proposed method combines the advantages and central ideas of very successful numerical techniques, the summationby-parts finite difference method, the spectral method and the discontinuous Galerkin method. We prove energy-stability, discrete conservation principle, and derive error estimates in the energy norm for the (1+1)-dimensions shifted wave equation in second order form. The energystability results, discrete conservation principle, and the error estimates generalise to multiple dimensions using tensor products of quadrilateral and hexahedral elements. Numerical experiments, in (1+1)-dimensions and (2+1)-dimensions, verify the theoretical results and demonstrate optimal convergence of L 2 numerical errors at subsonic, sonic and supersonic regimes.

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Derivative error bounds for Lagrange interpolation: An extension of Cauchy's bound for the error of Lagrange interpolation

Cited by 24 publications

References 4 publications

On Optimal Derivative Error Bounds for Lagrange Interpolation

On Optimal Derivative Error Bounds for Lagrange Interpolation

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

A conservative and energy stable discontinuous spectral element method for the shifted wave equation in second order form

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