English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

This paper is devoted to a new first order Taylor-like formula where thecorresponding remainder is strongly reduced in comparison with the usual onewhich appears in the classical Taylor's formula. To derive this new formula, weintroduce a linear combination of the first derivative of the concernedfunction, which is computed at n+1 equally-spaced points between the two pointswhere the function has to be evaluated. We show that an optimal choice of theweights in the linear combination leads to minimizing the correspondingremainder. Then, we analyze the Lagrange P1- interpolation error estimate andalso the trapezoidal quadrature error, in order to assess the gain of accuracywe obtain using this new Taylor-like formula.

A New First Order Taylor-like Theorem With An Optimized Reduced Remainder