Trigonometric multiple orthogonal polynomials of semi-integer degree and the corresponding quadrature formulas | Zendy

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

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Trigonometric multiple orthogonal polynomials of semi-integer degree and the corresponding quadrature formulas

Author(s) -

Gradimir V. Milovanović,

Marija P. Stanić,

Tatjana V. Tomović

Publication year - 2014

Publication title -

publications de l institut mathematique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.246

H-Index - 17

eISSN - 1820-7405

pISSN - 0350-1302

DOI - 10.2298/pim1410211m

Subject(s) - mathematics , orthogonal polynomials , trigonometry , trigonometric substitution , discrete orthogonal polynomials , quadrature (astronomy) , gauss–jacobi quadrature , orthogonality , classical orthogonal polynomials , trigonometric integral , proofs of trigonometric identities , gauss–kronrod quadrature formula , clenshaw–curtis quadrature , degree (music) , mathematical analysis , gaussian quadrature , nyström method , polynomial , integral equation , geometry , physics , linear interpolation , acoustics , optics , bicubic interpolation

An optimal set of quadrature formulas with an odd number of nodes for trigonometric polynomials in Borges’ sense [Numer. Math. 67 (1994), 271-288], as well as trigonometric multiple orthogonal polynomials of semi-integer degree are defined and studied. The main properties of such a kind of orthogonality are proved. Also, an optimal set of quadrature rules is characterized by trigonometric multiple orthogonal polynomials of semiinteger degree. Finally, theoretical results are illustrated by some numerical examples. [Projekat Ministarstva nauke Republike Srbije, br. 174015 i br. 44006]

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