Computing rational Gauss-Chebyshev quadrature formulas with complex poles: The algorithm
type: Item
instance of: scholarly article
title: Computing rational Gauss-Chebyshev quadrature formulas with complex poles: The algorithm
zbMATH Open document ID: 1173.65018
author: Karl Deckers
author: Adhemar Bultheel
author: Joris Van Deun
published in: Advances in Engineering Software
publication date: 2009-06-30T00:00:00Z
review text: The authors provide an algorithm to compute arbitrarily many nodes and weights for rational Gauss-Chebyshev quadrature formulas integrating exactly in spaces of rational functions with complex poles outside \([ - 1, 1]\). Contrary to existing rational quadrature formulas, the computational effort is very low, even for extremely high degrees, and under certain conditions on the poles it can be shown that the complexity is of order \(O(n)\). This algorithm is based on the derivation of explicit expressions for the Chebyshev (para-)orthogonal rational functions on \([ - 1, 1]\) with arbitrary complex poles outside this interval.
reviewed by: Dumitru Acu
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
zbMATH DE Number: 5572041
zbMATH Keywords: orthogonal rational functions
zbMATH Keywords: complex poles
zbMATH Keywords: algorithm
zbMATH Keywords: rational Gauss-Chebyshev quadrature formulas
zbMATH Keywords: complexity
MaRDI profile type: Publication
full work available at URL: j.advengsoft.2008.11.011
OpenAlex ID: W2058089454
cites work: Q5777281
cites work: Q3473612
cites work: Q4223056
cites work: Quadrature and orthogonal rational functions
cites work: State space representation for arbitrary orthogonal rational functions
cites work: Orthogonal rational matrix‐valued functions on the unit circle
cites work: Orthogonal rational matrix‐valued functions on the unit circle: Recurrence relations and a Favard‐type theorem
cites work: Build up of a Szegő theory for rational matrix functions
cites work: An interpolation algorithm for orthogonal rational functions.
cites work: Orthogonal rational functions and quadrature on an interval
cites work: Ratio asymptotics for orthogonal rational functions on an interval
cites work: A weak-star convergence result for orthogonal rational functions
cites work: Boundary asymptotics for orthogonal rational functions on the unit circle
cites work: Recurrence and asymptotics for orthonormal rational functions on an interval
cites work: An extended relation between orthogonal rational functions on the unit circle and the interval \([ - 1,1]\)
cites work: On computing rational Gauss-Chebyshev quadrature formulas
cites work: Rational Gauss-Chebyshev quadrature formulas for complex poles outside $[-1,1]$
DOI: 10.1016/J.ADVENGSOFT.2008.11.011
description: scientific article; zbMATH DE number 5572041