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.