Szegő-Lobatto quadrature rules
type: Item
instance of: scholarly article
title: Szegő-Lobatto quadrature rules
zbMATH Open document ID: 1109.65027
author: Carl Jagels
author: Lothar Reichel
published in: Journal of Computational and Applied Mathematics
publication date: 2007-01-22T00:00:00Z
review text: Szegö quadrature rules are analogs of Gauss quadrature rules for the integration of periodic functions. They integrate exactly trigonometric polynomials of as high degree as possible. Szegö quadrature rules have a free parameter, which can be used to prescribe one node. This paper discusses so-called Szegö-Lobatto rules, i.e., Szegö quadrature rules with 2 prescribed nodes. It is shown that Szegö-Lobatto rules exist and that, generally, they depend on a parameter which can be chosen on a circular arc. The nodes and weights of a Szegö-Lobatto rule are the eigenvalues and the squares of the first component of the normalized eigenvectors of a unitary upper Hessenberg matrix. The nodes and weights can be computed with software for the unitary eigenvalue problem for upper Hessenberg matrices.
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 41A55
zbMATH DE Number: 5117671
zbMATH Keywords: Szegö quadrature rule
zbMATH Keywords: Szegö-Lobatto quadrature rule
zbMATH Keywords: Szegö polynomial
zbMATH Keywords: upper Hessenberg matrix
zbMATH Keywords: eigenvalue problem
zbMATH Keywords: integration of periodic functions
zbMATH Keywords: trigonometric polynomials
reviewed by: Manfred Tasche
describes a project that uses: UDC
describes a project that uses: GAUSSIAN
describes a project that uses: pchip
describes a project that uses: OPQ
describes a project that uses: UNCMND
MaRDI profile type: Publication
full work available at URL: j.cam.2005.12.009
OpenAlex ID: W2074694609
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DOI: 10.1016/J.CAM.2005.12.009
description: scientific article; zbMATH DE number 5117671