On Gauss-type quadrature formulas with prescribed nodes anywhere on the real line

Keywords

Quadrature (astronomy), Numerical integration, Mathematics, Gauss–Kronrod quadrature formula, Gauss–Jacobi quadrature

References

• Nodes and weights of quadrature formulas : sixteen-place tablesAleksandr Semenovich Kronrod — 1965
• The Matrix Eigenvalue Problem: GR and Krylov Subspace MethodsDavid S. Watkins — 2007
• Some Optimal Runge‐Kutta Collocation Methods for Stiff Problems and DAEsS. González‐Pinto, D. Hernández‐Abreu, J.I. Montijano — 2008
• Characterization of Positive Quadrature FormulasFranz Peherstorfer — 1981
• On orthogonal polynomialsE.I. Jury, Seoiyoung Ahn — 1975
• Quasi-orthogonality with applications to some families of classical orthogonal polynomialsClaude Brezinski, K. Driver, Michela Redivo‐Zaglia — 2004
• Orthogonal polynomials: applications and computationWalter Gautschi — 1996
• Some results about numerical quadrature on the unit circlePablo González-Vera, J.C. Santos-León, Olav Njåstad — 1996
• Algorithm 726: ORTHPOL–a package of routines for generating orthogonal polynomials and Gauss-type quadrature rulesWalter Gautschi — 1994
• Moment Theory, Orthogonal Polynomials, Quadrature, and Continued Fractions Associated with the unit CircleWilliam B. Jones, Olav Njåstad, W. J. Thron — 1989
• On mechanical quadraturesJ. Shohat, Jacques Chokhate, C. Winston — 1934
• Positive definite Toeplitz matrices, the Arnoldi process for isometric operators, and Gaussian quadrature on the unit circleWilliam B. Gragg — 1993
• On mechanical quadratures, in particular, with positive coefficientsJ. Shohat — 1937
• Methods of Numerical IntegrationF. S., Philip J. Davis, Philip Rabinowitz — 1985
• Szegő-Lobatto quadrature rulesCarl Jagels, Lothar Reichel — 2007
• An efficient family of strongly A-stable Runge-Kutta collocation methods for stiff systems and DAEs. Part I: Stability and order resultsS. González‐Pinto, D. Hernández‐Abreu, J.I. Montijano — 2010
• On polynomials orthogonal with respect to particular variable-signed weight functionsGiovanni Monegato — 1980
• Some modified matrix eigenvalue problemsGene H. Golub — 1973
• Quadrature formulas on the unit circle with prescribed nodes and maximal domain of validityAdhemar Bultheel, Leyla Daruis, Pablo González-Vera — 2009
• A connection between quadrature formulas on the unit circle and the interval [ - 1,1]Adhemar Bultheel, Leyla Daruis, Pablo González-Vera — 2001

Cited by

• Computation of rational Szegő-Lobatto quadrature formulasAdhemar Bultheel, Pablo González-Vera, Erik Hendriksen — 2009
• Radau and Lobatto-type quadratures associated with strong Stieltjes distributionsCarlos Díaz Mendoza, Pablo González Vera, M. Jiménez Paiz — 2015
• Rational interpolation: II. Quadrature and convergenceKarl Deckers, Adhemar Bultheel — 2013
• The existence and construction of rational Gauss-type quadrature rulesKarl Deckers, Adhemar Bultheel — 2012
• An efficient family of strongly A-stable Runge-Kutta collocation methods for stiff systems and DAEs. Part I: Stability and order resultsS. González‐Pinto, D. Hernández‐Abreu, J.I. Montijano — 2010
• A connection between Szegő-Lobatto and quasi Gauss-type quadrature formulasRuymán Cruz‐Barroso, Carlos Díaz Mendoza, Francisco Perdomo-Pío — 2015
• Positive rational interpolatory quadrature formulas on the unit circle and the intervalKarl Deckers, Adhemar Bultheel, Ruymán Cruz‐Barroso — 2009
• Gaussian, Lobatto and Radau positive quadrature rules with a prescribed abscissaBernhard Beckermann, Jorge A. Bustamante, Reinaldo Martínez-Cruz — 2014
• Rational Gauss-Radau and rational Szegý o-Lobatto quadrature on the interval and the unit circle respectivelyKarl Deckers, Adhemar Bultheel — 2011
• Computation of Gauss-type quadrature formulas with some preassigned nodesAdhemar Bultheel, Ruymán Cruz Barroso, Pablo González-Vera — 2010
• Quasi-orthogonality of some hypergeometric polynomialsSarah Jane Johnston, A. Jooste, Kerstin Jordaan — 2016
• Bounds for Extreme Zeros of Quasi-orthogonal Ultraspherical PolynomialsKathy Driver, Martin E. Muldoon — 2016
• Numerical quadratures and orthogonal polynomialsGradimir V. Milovanović — 2011
• Zeros of quasi-orthogonal ultraspherical polynomialsKathy Driver, Martin E. Muldoon — 2016
• Rational interpolation and quadrature on the interval and on the unit circleKarl Deckers, Adhemar Bultheel — 2010
• On the computation of symmetric Szeg˝o-type quadrature formulasAdhemar Bultheel, Ruymán Cruz Barroso, Pablo González-Vera — 2010
• Numerical quadrature and orthogonal rational functionsAdhemar Bultheel — 2012
• Interlacing of zeros of quasi-orthogonal Meixner polynomialsK. Driver, A. Jooste — 2017
• One-sided weighted integral approximation of characteristic functions of intervals by polynomials on a closed intervalА. Г. Бабенко, M. V. Deikalova, Sz. Gy. Révész — 2017
• On spherical codes with inner products in a prescribed intervalPeter Boyvalenkov, Peter D Dragnev, Douglas P. Hardin — 2018

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