Multiple Orthogonality in the Space of Trigonometric Polynomials of Semi–Integer Degree

In this paper we consider multiple orthogonal trigonometric polynomials of semi–integer degree, which are necessary for constructing of an optimal set of quadrature rules with an odd number of nodes for trigonometric polynomials in Borges' sense [Numer. Math. 67 (1994) 271–288]. We prove that s...

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Bibliographic Details
Published in:Filomat 2015-01, Vol.29 (10), p.2227-2237
Main Authors: Stanic, Marija, Tomovic, Tatjana
Format: Article
Language:English
Subjects:
Algebra
Coefficients
Degrees of polynomials
Integers
Numerical quadratures
Orthogonality
Polynomials
Recurrence relations
Sine function
Weighting functions
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Summary:In this paper we consider multiple orthogonal trigonometric polynomials of semi–integer degree, which are necessary for constructing of an optimal set of quadrature rules with an odd number of nodes for trigonometric polynomials in Borges' sense [Numer. Math. 67 (1994) 271–288]. We prove that such multiple orthogonal trigonometric polynomials satisfy certain recurrence relations and present numerical method for their construction, as well as for construction of mentioned optimal set of quadrature rules. Theoretical results are illustrated by some numerical examples
ISSN:0354-5180
2406-0933
DOI:10.2298/FIL1510227S