{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T08:55:37Z","timestamp":1776848137046,"version":"3.51.2"},"reference-count":33,"publisher":"American Mathematical Society (AMS)","issue":"266","license":[{"start":{"date-parts":[[2009,12,9]],"date-time":"2009-12-09T00:00:00Z","timestamp":1260316800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>In this paper we characterize rational Szeg\u0151 quadrature formulas associated with Chebyshev weight functions, by giving explicit expressions for the corresponding para-orthogonal rational functions and weights in the quadratures. As an application, we give characterizations for Szeg\u0151 quadrature formulas associated with rational modifications of Chebyshev weight functions. Some numerical experiments are finally presented.<\/p>","DOI":"10.1090\/s0025-5718-08-02208-4","type":"journal-article","created":{"date-parts":[[2009,12,1]],"date-time":"2009-12-01T13:09:23Z","timestamp":1259672963000},"page":"1031-1059","source":"Crossref","is-referenced-by-count":16,"title":["Rational Szego quadratures associated with Chebyshev weight functions"],"prefix":"10.1090","volume":"78","author":[{"given":"Adhemar","family":"Bultheel","sequence":"first","affiliation":[]},{"given":"Ruym\u00e1n","family":"Cruz-Barroso","sequence":"additional","affiliation":[]},{"given":"Karl","family":"Deckers","sequence":"additional","affiliation":[]},{"given":"Pablo","family":"Gonz\u00e1lez-Vera","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2008,12,9]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0377-0427(00)00594-X","article-title":"A connection between quadrature formulas on the unit circle and the interval [-1,1]","volume":"132","author":"Bultheel, Adhemar","year":"2001","journal-title":"J. Comput. Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0377-0427","issn-type":"print"},{"issue":"1-2","key":"2","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1016\/j.cam.2004.09.037","article-title":"Positive interpolatory quadrature formulas and para-orthogonal polynomials","volume":"179","author":"Bultheel, Adhemar","year":"2005","journal-title":"J. Comput. Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0377-0427","issn-type":"print"},{"issue":"1-4","key":"3","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1007\/BF02141920","article-title":"Orthogonal rational functions and quadrature on the unit circle","volume":"3","author":"Bultheel, Adhemar","year":"1992","journal-title":"Numer. Algorithms","ISSN":"https:\/\/id.crossref.org\/issn\/1017-1398","issn-type":"print"},{"issue":"1-3","key":"4","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1016\/0377-0427(94)90297-6","article-title":"Quadrature formulas on the unit circle based on rational functions","volume":"50","author":"Bultheel, Adhemar","year":"1994","journal-title":"J. Comput. Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0377-0427","issn-type":"print"},{"key":"5","series-title":"Cambridge Monographs on Applied and Computational Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511530050","volume-title":"Orthogonal rational functions","volume":"5","author":"Bultheel, Adhemar","year":"1999","ISBN":"https:\/\/id.crossref.org\/isbn\/0521650062"},{"issue":"1-2","key":"6","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1016\/S0377-0427(00)00493-3","article-title":"Quadrature and orthogonal rational functions","volume":"127","author":"Bultheel, A.","year":"2001","journal-title":"J. Comput. Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0377-0427","issn-type":"print"},{"key":"7","unstructured":"\\bysame, Rational quadrature formulas on the unit circle with prescribed nodes and maximal domain of validity, (2007), Submitted."},{"issue":"3","key":"8","doi-asserted-by":"publisher","first-page":"296","DOI":"10.1016\/j.apnum.2006.11.009","article-title":"A matrix approach to the computation of quadrature formulas on the unit circle","volume":"58","author":"Cantero, Mar\u00eda Jos\u00e9","year":"2008","journal-title":"Appl. Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0168-9274","issn-type":"print"},{"issue":"2","key":"9","doi-asserted-by":"publisher","first-page":"950","DOI":"10.1016\/j.cam.2006.09.003","article-title":"Sequences of orthogonal Laurent polynomials, bi-orthogonality and quadrature formulas on the unit circle","volume":"206","author":"Cruz-Barroso, Ruym\u00e1n","year":"2007","journal-title":"J. Comput. Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0377-0427","issn-type":"print"},{"issue":"1","key":"10","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1016\/S0168-9274(99)00136-1","article-title":"Szeg\u0151 polynomials and quadrature formulas on the unit circle","volume":"36","author":"Daruis, Leyla","year":"2001","journal-title":"Appl. Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0168-9274","issn-type":"print"},{"issue":"238","key":"11","doi-asserted-by":"publisher","first-page":"683","DOI":"10.1090\/S0025-5718-01-01337-0","article-title":"Szeg\u00f6 quadrature formulas for certain Jacobi-type weight functions","volume":"71","author":"Daruis, Leyla","year":"2002","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"3-4","key":"12","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1016\/j.camwa.2005.10.004","article-title":"Quadrature formulas associated with rational modifications of the Chebyshev weight functions","volume":"51","author":"Daruis, L.","year":"2006","journal-title":"Comput. Math. Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/0898-1221","issn-type":"print"},{"key":"13","volume-title":"Interpolation and approximation","author":"Davis, Philip J.","year":"1975"},{"key":"14","doi-asserted-by":"crossref","unstructured":"K. Deckers and A. Bultheel, Orthogonal rational functions and rational modifications of a measure on the unit circle, J. Approx. Theory (2008), Accepted.","DOI":"10.1016\/j.jat.2008.04.017"},{"key":"15","unstructured":"K. Deckers, J. Van Deun, and A. Bultheel, Computing rational Gauss-Chebyshev quadrature formulas with complex poles, Proceedings of the Fifth International Conference on Engineering Computational Technology (Kippen, Stirlingshire, United Kingdom) (B.H.V. Topping, G. Montero, and R. Montenegro, eds.), Civil-Comp Press, 2006, Paper 30."},{"issue":"2","key":"16","doi-asserted-by":"publisher","first-page":"1260","DOI":"10.1016\/j.jmaa.2007.01.031","article-title":"An extended relation between orthogonal rational functions on the unit circle and the interval [-1,1]","volume":"334","author":"Deckers, Karl","year":"2007","journal-title":"J. Math. Anal. Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/0022-247X","issn-type":"print"},{"key":"17","unstructured":"\\bysame, Computing rational Gauss-Chebyshev quadrature formulas with complex poles: the algorithm, Advances in Engineering Software (2008), Accepted."},{"issue":"262","key":"18","doi-asserted-by":"publisher","first-page":"967","DOI":"10.1090\/S0025-5718-07-01982-5","article-title":"Rational Gauss-Chebyshev quadrature formulas for complex poles outside [-1,1]","volume":"77","author":"Deckers, Karl","year":"2008","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"19","isbn-type":"print","first-page":"72","article-title":"A survey of Gauss-Christoffel quadrature formulae","author":"Gautschi, Walter","year":"1981","ISBN":"https:\/\/id.crossref.org\/isbn\/3764311622"},{"issue":"4","key":"20","doi-asserted-by":"publisher","first-page":"617","DOI":"10.1007\/PL00005412","article-title":"Quadrature rules for rational functions","volume":"86","author":"Gautschi, Walter","year":"2000","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"key":"21","series-title":"International Series of Monographs on Pure and Applied Mathematics, Vol. 18","volume-title":"Polynomials orthogonal on a circle and interval","author":"Geronimus, Ja. L.","year":"1960"},{"issue":"1-2","key":"22","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1016\/0377-0427(93)90294-L","article-title":"Positive definite Toeplitz matrices, the Arnoldi process for isometric operators, and Gaussian quadrature on the unit circle","volume":"46","author":"Gragg, William B.","year":"1993","journal-title":"J. Comput. Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0377-0427","issn-type":"print"},{"key":"23","series-title":"California Monographs in Mathematical Sciences","doi-asserted-by":"crossref","DOI":"10.1525\/9780520355408","volume-title":"Toeplitz forms and their applications","author":"Grenander, Ulf","year":"1958"},{"issue":"1","key":"24","doi-asserted-by":"publisher","first-page":"116","DOI":"10.1016\/j.cam.2005.12.009","article-title":"Szeg\u0151-Lobatto quadrature rules","volume":"200","author":"Jagels, Carl","year":"2007","journal-title":"J. Comput. Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0377-0427","issn-type":"print"},{"issue":"2","key":"25","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1112\/blms\/21.2.113","article-title":"Moment theory, orthogonal polynomials, quadrature, and continued fractions associated with the unit circle","volume":"21","author":"Jones, William B.","year":"1989","journal-title":"Bull. London Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0024-6093","issn-type":"print"},{"key":"26","series-title":"American Mathematical Society Colloquium Publications","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1090\/coll054.1","volume-title":"Orthogonal polynomials on the unit circle. Part 1","volume":"54","author":"Simon, Barry","year":"2005","ISBN":"https:\/\/id.crossref.org\/isbn\/0821834460"},{"key":"27","first-page":"255","article-title":"On bi-orthogonal systems of trigonometric polynomials","volume":"8","author":"Szeg\u00f6, G\u00e1bor","year":"1964","journal-title":"Magyar Tud. Akad. Mat. Kutat\\'{o} Int. K\\\"{o}zl.","ISSN":"https:\/\/id.crossref.org\/issn\/0541-9514","issn-type":"print"},{"key":"28","unstructured":"\\bysame, Orthogonal polynomials, 4th ed., Amer. Math. Soc. Colloq. Publ., vol. 33, Amer. Math. Soc., Providence, Rhode Island, 1975."},{"issue":"204","key":"29","doi-asserted-by":"publisher","first-page":"765","DOI":"10.2307\/2153252","article-title":"Quadrature formulas based on rational interpolation","volume":"61","author":"Van Assche, Walter","year":"1993","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"253","key":"30","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1090\/S0025-5718-05-01774-6","article-title":"On computing rational Gauss-Chebyshev quadrature formulas","volume":"75","author":"Van Deun, Joris","year":"2006","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"31","doi-asserted-by":"crossref","unstructured":"J. Van Deun, K. Deckers, A. Bultheel, and J.A.C. Weideman, Algorithm 882: Near best fixed pole rational interpolation with applications in spectral methods, ACM Trans. Math. Software 32 (2008), no. 2, article no. 14, pp. 1\u201321.","DOI":"10.1145\/1377612.1377618"},{"key":"32","first-page":"170","article-title":"A relation between orthogonal rational functions on the unit circle and the interval [-1,1]","volume":"8","author":"Van Gucht, Patrick","year":"2000","journal-title":"Commun. Anal. Theory Contin. Fract."},{"key":"33","isbn-type":"print","first-page":"479","article-title":"A Szeg\u0151 quadrature formula for the Poisson formula","author":"Waadeland, Haakon","year":"1992","ISBN":"https:\/\/id.crossref.org\/isbn\/0444897011"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2009-78-266\/S0025-5718-08-02208-4\/S0025-5718-08-02208-4.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2009-78-266\/S0025-5718-08-02208-4\/S0025-5718-08-02208-4.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T15:57:50Z","timestamp":1776787070000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2009-78-266\/S0025-5718-08-02208-4\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,12,9]]},"references-count":33,"journal-issue":{"issue":"266","published-print":{"date-parts":[[2009,4]]}},"alternative-id":["S0025-5718-08-02208-4"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-08-02208-4","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2008,12,9]]}}}