Positive trigonometric Quadrature Formulas and quadrature on the unit circle

Franz Peherstorfer

Positive trigonometric Quadrature Formulas and quadrature on the unit circle

Classical Analysis and ODEs 2010-01-15 v1 Complex Variables

Authors: Franz Peherstorfer

Abstract

We give several descriptions of positive quadrature formulas which are exact for trigonometric -, respectively, Laurent polynomials of degree less or equal $n-1-m$ , $0\leq m\leq n-1$ . A complete and simple description is obtained with the help of orthogonal polynomials on the unit circle. In particular it is shown that the nodes polynomial can be generated by a simple recurrence relation. As a byproduct interlacing properties of zeros of para-orthogonal polynomials are obtained. Finally, asymptotics for the quadrature weights are presented.

Keywords

positive quadrature formulas trigonometric polynomials Laurent polynomials orthogonal polynomials on the unit circle para-orthogonal polynomials interlacing properties quadrature weights asymptotics

Cite

@article{arxiv.1001.2451,
  title  = {Positive trigonometric Quadrature Formulas and quadrature on the unit circle},
  author = {Franz Peherstorfer},
  journal= {arXiv preprint arXiv:1001.2451},
  year   = {2010}
}

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Submitted by F. Peherstorfer to Math. Comp

Positive trigonometric Quadrature Formulas and quadrature on the unit circle

Abstract

Keywords

Cite

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