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Multiple orhogonality in the space of trigonometric polynomials if semi--integer degree
Last modified: 2014-01-02
Abstract
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. {\bf67} (1994), 271--288]. We prove that such multiple orthogonal trigonometric polynomials satisfy certain recurrence relation 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.
for trigonometric polynomials in Borges' sense [Numer. Math. {\bf67} (1994), 271--288]. We prove that such multiple orthogonal trigonometric polynomials satisfy certain recurrence relation 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.
Keywords
multiple orthogonal trigonometric polynomials; recurrence relations; optimal set of quadrature rules