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Volume 22, Issue 6
Optimized First-Order Taylor-Like Formulas and Gauss Quadrature Errors

Joël Chaskalovic & Franck Assous

DOI: 10.4208/ijnam2025-1036

Int. J. Numer. Anal. Mod., 22 (2025), pp. 824-842.

Published online: 2025-08

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  • Abstract

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.

  • Keywords

Taylor’s theorem, Taylor-like formula, error estimate, interpolation error, approximation error, finite elements.

  • AMS Subject Headings

65N30,78M10,35B65,35L67

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@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 = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2025-1036}, url = {http://global-sci.org/intro/article_detail/ijnam/24295.html} }
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 -

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.

Chaskalovic , Joël and Assous , Franck. (2025). Optimized First-Order Taylor-Like Formulas and Gauss Quadrature Errors. International Journal of Numerical Analysis and Modeling. 22 (6). 824-842. doi:10.4208/ijnam2025-1036
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