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Article Dans Une Revue Journal of Computational and Applied Mathematics Année : 2024

A new second order Taylor-like theorem with an optimized reduced remainder

Joël Chaskalovic
Franck Assous
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Résumé

In this paper, we derive a variant of the Taylor theorem to obtain a new minimized remainder. For a given function f defined on the interval [a, b], this formula is derived by introducing a linear combination of f ′ computed at n + 1 equally spaced points in [a, b], together with f ′′ (a) and f ′′ (b). We then consider two classical applications of this Taylor-like expansion: the interpolation error and the numerical quadrature formula. We show that using this approach improves both the Lagrange P 2-interpolation error estimate and the error bound of the Simpson rule in numerical integration.
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Dates et versions

hal-04196065 , version 1 (02-05-2023)
hal-04196065 , version 2 (06-09-2023)

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Joël Chaskalovic, Franck Assous, Hessam Jamshidipour. A new second order Taylor-like theorem with an optimized reduced remainder. Journal of Computational and Applied Mathematics, 2024, 438, ⟨10.1016/j.cam.2023.115496⟩. ⟨hal-04196065v2⟩
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