Year: 2014
Author: Zhongxuan Luo, Ran Yu, Zhaoliang Meng
Communications in Mathematical Research , Vol. 30 (2014), Iss. 4 : pp. 334–344
Abstract
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 $m ≥ 3$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.13447/j.1674-5647.2014.04.07
Communications in Mathematical Research , Vol. 30 (2014), Iss. 4 : pp. 334–344
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: quadrature formula trigonometric function bi-orthogonality truncated complex moment problem.