@Article{CMR-30-4,
author = {Zhongxuan, Luo and Yu, Ran and Zhaoliang, Meng},
title = {The Maximum Trigonometric Degrees of Quadrature Formulae with Prescribed Nodes},
journal = {Communications in Mathematical Research },
year = {2014},
volume = {30},
number = {4},
pages = {334--344},
abstract = {<p style="text-align: justify;">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 $m ≥ 3$.</p>},
issn = {2707-8523},
doi = {https://doi.org/10.13447/j.1674-5647.2014.04.07},
url = {https://global-sci.com/article/81767/the-maximum-trigonometric-degrees-of-quadrature-formulae-with-prescribed-nodes}
}