@Article{IJNAM-22-824,
author = {Chaskalovic , Joël and Assous , Franck},
title = {Optimized First-Order Taylor-Like Formulas and Gauss Quadrature Errors},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2025},
volume = {22},
number = {6},
pages = {824--842},
abstract = {<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>},
issn = {2617-8710},
doi = {https://doi.org/10.4208/ijnam2025-1036},
url = {http://global-sci.org/intro/article_detail/ijnam/24295.html}
}