- Journal Home
- Volume 41 - 2025
- Volume 40 - 2024
- Volume 39 - 2023
- Volume 38 - 2022
- Volume 37 - 2021
- Volume 36 - 2020
- Volume 35 - 2019
- Volume 34 - 2018
- Volume 33 - 2017
- Volume 32 - 2016
- Volume 31 - 2015
- Volume 30 - 2014
- Volume 29 - 2013
- Volume 28 - 2012
- Volume 27 - 2011
- Volume 26 - 2010
- Volume 25 - 2009
Commun. Math. Res., 30 (2014), pp. 334-344.
Published online: 2021-05
Cited by
- BibTex
- RIS
- TXT
The purpose of this paper is to study the maximum trigonometric degree of the quadrature formula associated with $m$ prescribed nodes and $n$ unknown additional nodes in the interval $(−π, π]$. We show that for a fixed $n$, the quadrature formulae with $m$ and $m + 1$ prescribed nodes share the same maximum degree if $m$ is odd. We also give necessary and sufficient conditions for all the additional nodes to be real, pairwise distinct and in the interval $(−π, π]$ for even $m$, which can be obtained constructively. Some numerical examples are given by choosing the prescribed nodes to be the zeros of Chebyshev polynomials of the second kind or randomly for $m ≥ 3$.
}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2014.04.07}, url = {http://global-sci.org/intro/article_detail/cmr/18957.html} }The purpose of this paper is to study the maximum trigonometric degree of the quadrature formula associated with $m$ prescribed nodes and $n$ unknown additional nodes in the interval $(−π, π]$. We show that for a fixed $n$, the quadrature formulae with $m$ and $m + 1$ prescribed nodes share the same maximum degree if $m$ is odd. We also give necessary and sufficient conditions for all the additional nodes to be real, pairwise distinct and in the interval $(−π, π]$ for even $m$, which can be obtained constructively. Some numerical examples are given by choosing the prescribed nodes to be the zeros of Chebyshev polynomials of the second kind or randomly for $m ≥ 3$.