1. A new second order Taylor-like theorem with an optimized reduced remainder
- Author
-
Chaskalovic, J. and Assous, F.
- Subjects
FOS: Mathematics ,Mathematics - Numerical Analysis ,Numerical Analysis (math.NA) ,65D30, 65N15, 65N30, 65N75, 41A05 - Abstract
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.
- Published
- 2023
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