The natural algorithmic approach of mixed trigonometric-polynomial problems

The aim of this paper is to present a new algorithm for proving mixed trigonometric-polynomial inequalities of the form [Formula: see text] by reducing them to polynomial inequalities. Finally, we show the great applicability of this algorithm and, as an example, we use it to analyze some new ration...

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Detalles Bibliográficos
Autores principales: Lutovac, Tatjana, Malešević, Branko, Mortici, Cristinel
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5437218/
https://www.ncbi.nlm.nih.gov/pubmed/28596694
http://dx.doi.org/10.1186/s13660-017-1392-1
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author Lutovac, Tatjana
Malešević, Branko
Mortici, Cristinel
author_facet Lutovac, Tatjana
Malešević, Branko
Mortici, Cristinel
author_sort Lutovac, Tatjana
collection PubMed
description The aim of this paper is to present a new algorithm for proving mixed trigonometric-polynomial inequalities of the form [Formula: see text] by reducing them to polynomial inequalities. Finally, we show the great applicability of this algorithm and, as an example, we use it to analyze some new rational (Padé) approximations of the function cos(2) x and to improve a class of inequalities by Yang. The results of our analysis could be implemented by means of an automated proof assistant, so our work is a contribution to the library of automatic support tools for proving various analytic inequalities.
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spelling pubmed-54372182017-06-06 The natural algorithmic approach of mixed trigonometric-polynomial problems Lutovac, Tatjana Malešević, Branko Mortici, Cristinel J Inequal Appl Research The aim of this paper is to present a new algorithm for proving mixed trigonometric-polynomial inequalities of the form [Formula: see text] by reducing them to polynomial inequalities. Finally, we show the great applicability of this algorithm and, as an example, we use it to analyze some new rational (Padé) approximations of the function cos(2) x and to improve a class of inequalities by Yang. The results of our analysis could be implemented by means of an automated proof assistant, so our work is a contribution to the library of automatic support tools for proving various analytic inequalities. Springer International Publishing 2017-05-18 2017 /pmc/articles/PMC5437218/ /pubmed/28596694 http://dx.doi.org/10.1186/s13660-017-1392-1 Text en © The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Lutovac, Tatjana
Malešević, Branko
Mortici, Cristinel
The natural algorithmic approach of mixed trigonometric-polynomial problems
title The natural algorithmic approach of mixed trigonometric-polynomial problems
title_full The natural algorithmic approach of mixed trigonometric-polynomial problems
title_fullStr The natural algorithmic approach of mixed trigonometric-polynomial problems
title_full_unstemmed The natural algorithmic approach of mixed trigonometric-polynomial problems
title_short The natural algorithmic approach of mixed trigonometric-polynomial problems
title_sort natural algorithmic approach of mixed trigonometric-polynomial problems
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5437218/
https://www.ncbi.nlm.nih.gov/pubmed/28596694
http://dx.doi.org/10.1186/s13660-017-1392-1
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