Positive trigonometric Quadrature Formulas and quadrature on the unit\n circle

2010/01/14 by Franz Peherstorfer, Peherstorfer, Franz
Computer Science · Mathematics · Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #Electromagnetic Scattering and Analysis #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.1001.2451

openalex publication_date 2010/01/14 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Moment Theory, Orthogonal Polynomials, Quadrature, and Continued Fractions Associated with the unit Circle

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