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Numerical Algorithms

, Volume 44, Issue 4, pp 309–333 | Cite as

On bi-orthogonal systems of trigonometric functions and quadrature formulas for periodic integrands

  • Ruymán Cruz-Barroso
  • Pablo González-Vera
  • Olav Njåstad
Original Paper

Abstract

In this paper, quadrature formulas with an arbitrary number of nodes and exactly integrating trigonometric polynomials up to degree as high as possible are constructed in order to approximate 2π-periodic weighted integrals. For this purpose, certain bi-orthogonal systems of trigonometric functions are introduced and their most relevant properties studied. Some illustrative numerical examples are also given. The paper completes the results previously given by Szegő in Magy Tud Akad Mat Kut Intez Közl 8:255–273, 1963 and by some of the authors in Annales Mathematicae et Informaticae 32:5–44, 2005.

Keywords

Bi-orthogonality Quadrature rules Szegő polynomials Trigonometric functions 

Mathematics Subject Classifications (2000)

41A05 42A15 65D30 65D32 

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Copyright information

© Springer Science+Business Media LLC 2007

Authors and Affiliations

  • Ruymán Cruz-Barroso
    • 1
  • Pablo González-Vera
    • 1
  • Olav Njåstad
    • 2
  1. 1.Department of Mathematical AnalysisLa Laguna UniversityLa LagunaSpain
  2. 2.Department of Mathematical SciencesNorwegian University of Science and TechnologyTrondheimNorway

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