The Trigonometric Polynomial Like Bernstein Polynomial

A symmetric basis of trigonometric polynomial space is presented. Based on the basis, symmetric trigonometric polynomial approximants like Bernstein polynomials are constructed. Two kinds of nodes are given to show that the trigonometric polynomial sequence is uniformly convergent. The convergence o...

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Detalles Bibliográficos
Autor principal: Han, Xuli
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4165195/
https://www.ncbi.nlm.nih.gov/pubmed/25276845
http://dx.doi.org/10.1155/2014/174716
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author Han, Xuli
author_facet Han, Xuli
author_sort Han, Xuli
collection PubMed
description A symmetric basis of trigonometric polynomial space is presented. Based on the basis, symmetric trigonometric polynomial approximants like Bernstein polynomials are constructed. Two kinds of nodes are given to show that the trigonometric polynomial sequence is uniformly convergent. The convergence of the derivative of the trigonometric polynomials is shown. Trigonometric quasi-interpolants of reproducing one degree of trigonometric polynomials are constructed. Some interesting properties of the trigonometric polynomials are given.
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spelling pubmed-41651952014-09-28 The Trigonometric Polynomial Like Bernstein Polynomial Han, Xuli ScientificWorldJournal Research Article A symmetric basis of trigonometric polynomial space is presented. Based on the basis, symmetric trigonometric polynomial approximants like Bernstein polynomials are constructed. Two kinds of nodes are given to show that the trigonometric polynomial sequence is uniformly convergent. The convergence of the derivative of the trigonometric polynomials is shown. Trigonometric quasi-interpolants of reproducing one degree of trigonometric polynomials are constructed. Some interesting properties of the trigonometric polynomials are given. Hindawi Publishing Corporation 2014 2014-08-27 /pmc/articles/PMC4165195/ /pubmed/25276845 http://dx.doi.org/10.1155/2014/174716 Text en Copyright © 2014 Xuli Han. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Han, Xuli
The Trigonometric Polynomial Like Bernstein Polynomial
title The Trigonometric Polynomial Like Bernstein Polynomial
title_full The Trigonometric Polynomial Like Bernstein Polynomial
title_fullStr The Trigonometric Polynomial Like Bernstein Polynomial
title_full_unstemmed The Trigonometric Polynomial Like Bernstein Polynomial
title_short The Trigonometric Polynomial Like Bernstein Polynomial
title_sort trigonometric polynomial like bernstein polynomial
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4165195/
https://www.ncbi.nlm.nih.gov/pubmed/25276845
http://dx.doi.org/10.1155/2014/174716
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AT hanxuli trigonometricpolynomiallikebernsteinpolynomial

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