<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>We present an adaptive method of approximate integration of convex (as well as concave) functions based on a certain refinement of the celebrated Hermite–Hadamard inequality. Numerical experiments are performed and the role of harmonic numbers is shown.</p>
</abstract>

We present an adaptive method of approximate integration of convex (as well as concave) functions based on a certain refinement of the celebrated Hermite–Hadamard inequality. Numerical experiments are performed and the role of harmonic numbers is shown.

Adaptive Integration of Convex Functions of One Real Variable

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"Adaptive Integration of Convex Functions of One Real Variable"}

We present an adaptive method of approximate integration of convex (as well as concave) functions based on a certain refinement of the celebrated...

Adaptive Integration of Convex Functions of One Real Variable

Published Online: Jan 10, 2024

Page range: 120 - 133

Received: Jul 14, 2023

Accepted: Dec 18, 2023

DOI: https://doi.org/10.2478/amsil-2023-0028

Keywords
adaptive integration, convex function, Hermite–Hadamard inequality, quadrature, midpoint rule, trapezoid rule

© 2023 Szymon Wąsowicz, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Adaptive Integration of Convex Functions of One Real Variable

Published Online: Jan 10, 2024

Page range: 120 - 133

Received: Jul 14, 2023

Accepted: Dec 18, 2023

DOI: https://doi.org/10.2478/amsil-2023-0028

Keywordsadaptive integration, convex function, Hermite–Hadamard inequality, quadrature, midpoint rule, trapezoid rule

© 2023 Szymon Wąsowicz, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
adaptive integration, convex function, Hermite–Hadamard inequality, quadrature, midpoint rule, trapezoid rule