Multiple orthogonality in the space of trigonometric polynomials of semi-integer degree | Zendy

Marija P. Stanić | Zendy; Tatjana V. Tomović | Zendy

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Multiple orthogonality in the space of trigonometric polynomials of semi-integer degree

Author(s) -

Marija P. Stanić,

Tatjana V. Tomović

Publication year - 2015

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1510227s

Subject(s) - mathematics , trigonometry , orthogonality , orthogonal polynomials , discrete orthogonal polynomials , proofs of trigonometric identities , classical orthogonal polynomials , quadrature (astronomy) , degree (music) , trigonometric substitution , trigonometric integral , trigonometric polynomial , integer (computer science) , wilson polynomials , discrete mathematics , pure mathematics , mathematical analysis , polynomial , geometry , computer science , physics , linear interpolation , acoustics , electrical engineering , bicubic interpolation , programming language , engineering

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.

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