TY - JOUR
T1 - Optimized First-Order Taylor-Like Formulas and Gauss Quadrature Errors
AU - Chaskalovic , Joël
AU - Assous , Franck
JO - International Journal of Numerical Analysis and Modeling
VL - 6
SP - 824
EP - 842
PY - 2025
DA - 2025/08
SN - 22
DO - http://doi.org/10.4208/ijnam2025-1036
UR - https://global-sci.org/intro/article_detail/ijnam/24295.html
KW - Taylor’s theorem, Taylor-like formula, error estimate, interpolation error, approximation error, finite elements.
AB - <p style="text-align: justify;">In this article, we derive an optimal first-order Taylor-like formula. In a seminal
paper [15], we introduced a new first-order Taylor-like formula that yields a reduced remainder
compared to the classical Taylor’s formula. In this work, we relax the assumption of equally
spaced points in our formula. Instead, we consider a sequence of unknown points and a sequence
of unknown weights. We then solve an optimization problem to determine the optimal distribution
of points and weights that minimizes the corresponding remainder. Numerical results are provided
to illustrate our findings.</p>