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The Maximum Trigonometric Degrees of Quadrature Formulae with Prescribed Nodes

The Maximum Trigonometric Degrees of Quadrature Formulae with Prescribed Nodes

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.

Author Details

Zhongxuan Luo

Ran Yu

Zhaoliang Meng