{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T05:10:34Z","timestamp":1776834634010,"version":"3.51.2"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[1996,2,1]],"date-time":"1996-02-01T00:00:00Z","timestamp":823132800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[1996,2]]},"DOI":"10.1007\/bf02207699","type":"journal-article","created":{"date-parts":[[2005,10,5]],"date-time":"2005-10-05T22:15:45Z","timestamp":1128550545000},"page":"321-344","source":"Crossref","is-referenced-by-count":10,"title":["On the convergence of multipoint Pad\u00e9-type approximants and quadrature formulas associated with the unit circle"],"prefix":"10.1007","volume":"13","author":[{"given":"A.","family":"Bultheel","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.","family":"Gonz\u00e1lez-Vera","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"E.","family":"Hendriksen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"O.","family":"Nj\u00e5stad","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"BF02207699_CR1","volume-title":"Theory of Approximation","author":"N. I. Achieser","year":"1956","unstructured":"N. I. Achieser,Theory of Approximation (Frederick Ungar, New York, 1956)."},{"key":"BF02207699_CR2","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1007\/BF02141920","volume":"3","author":"A. Bultheel","year":"1992","unstructured":"A. Bultheel, P. Gonz\u00e1lez-Vera, E. Hendriksen and O. Nj\u00e5stad, Orthogonal rational functions and quadrature on the unit circle, Numer. Algorithms 3 (1992) 105\u2013116.","journal-title":"Numer. Algorithms"},{"key":"BF02207699_CR3","doi-asserted-by":"crossref","unstructured":"A. Bultheel, P. Gonz\u00e1lez-Vera, E. Hendriksen and O. Nj\u00e5stad, Orthogonality and boundary interpolation, in:Nonlinear Numerical Methods and Rational Approximation II, ed. A. M. Cuyt (Kluwer, 1994) pp. 37\u201348.","DOI":"10.1007\/978-94-011-0970-3_4"},{"key":"BF02207699_CR4","doi-asserted-by":"crossref","unstructured":"A. Bultheel, P. Gonz\u00e1lez-Vera, E. Hendriksen and O. Nj\u00e5stad, Quadrature formulas on the unit circle and two-point Pad\u00e9 approximation, in:Nonlinear Numerical Methods and Rational Approximation II, ed. A. M. Cuyt (Kluwer, 1994) pp. 303\u2013318.","DOI":"10.1007\/978-94-011-0970-3_26"},{"key":"BF02207699_CR5","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/0377-0427(94)90297-6","volume":"50","author":"A. Bultheel","year":"1994","unstructured":"A. Bultheel, P. Gonz\u00e1lez-Vera, E. Hendriksen and O. Nj\u00e5stad, Quadrature formulas on the unit circle based on rational functions, J. Comput. Appl. Math. 50 (1994) 159\u2013170.","journal-title":"J. Comput. Appl. Math."},{"key":"BF02207699_CR6","doi-asserted-by":"crossref","unstructured":"E. W. Cheney,Introduction to Approximation Theory (McGraw Hill, 1966).","DOI":"10.2307\/2314671"},{"key":"BF02207699_CR7","series-title":"Mathematical and Physical Sciences, Series C 294","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1007\/978-94-009-0501-6_6","volume-title":"Orthogonal Polynomials: Theory and Practice","author":"M. M. Djrbashian","year":"1990","unstructured":"M. M. Djrbashian, A survey on the theory of orthogonal systems and some open problems, in:Orthogonal Polynomials: Theory and Practice, ed. P. Nevai, Mathematical and Physical Sciences, Series C 294 (NATO-ASI, Kluwer, Boston, 1990) pp. 135\u2013146."},{"key":"BF02207699_CR8","doi-asserted-by":"crossref","unstructured":"W. Gautschi, Gauss-type quadrature rules for rational functions, in:Numerical Integration IV, eds. H. Brass and G. Hammerlin, Internat. Ser. Numer. Math. 112 (1993) pp. 111\u2013130.","DOI":"10.1007\/978-3-0348-6338-4_9"},{"key":"BF02207699_CR9","doi-asserted-by":"crossref","first-page":"930","DOI":"10.4153\/CJM-1993-052-1","volume":"45","author":"E. Godoy","year":"1993","unstructured":"E. Godoy and F. Marcellan, Orthogonal polynomials and rational modification of measures, Canad. J. Math. 45 (1993) 930\u2013943.","journal-title":"Canad. J. Math."},{"key":"BF02207699_CR10","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1070\/SM1986v053n01ABEH002912","volume":"53","author":"A. A. Gonchar","year":"1986","unstructured":"A. A. Gonchar and E. A. Rakhmanov, Equilibrium measure and the distribution of zeros of extremal polynomials, Math. USSR-Sb. 53 (1986) 119\u2013130.","journal-title":"Math. USSR-Sb."},{"key":"BF02207699_CR11","doi-asserted-by":"crossref","first-page":"747","DOI":"10.1006\/jmaa.1996.0345","volume":"202","author":"P. Gonz\u00e1lez-Vera","year":"1996","unstructured":"P. Gonz\u00e1lez-Vera, M. Jim\u00e9nez-P\u00e1iz, G. L\u00f3pez-Lagomasino and R. Orive, On the convergence of quadrature formulas connected with multipoint Pad\u00e9-type approximants, J. Math. Anal. Appl. 202 (1996) 747\u2013775.","journal-title":"J. Math. Anal. Appl."},{"key":"BF02207699_CR12","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1006\/jmaa.1995.1033","volume":"189","author":"P. Gonz\u00e1lez-Vera","year":"1995","unstructured":"P. Gonz\u00e1lez-Vera, G. L\u00f3pez-Lagomasino, R. Orive and J. C. Santos-Leon, On the convergence of quadrature formulas for complex weight functions, J. Math. Anal. Appl. 189 (1995) 514\u2013532.","journal-title":"J. Math. Anal. Appl."},{"key":"BF02207699_CR13","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/BF02124749","volume":"5","author":"P. Gonz\u00e1lez-Vera","year":"1996","unstructured":"P. Gonz\u00e1lez-Vera, O. Nj\u00e5stad and J.C. Santos-Leon, Some numerical results about quadrature formulas on the unit circle, Adv. Comput. Math. 5 (1996) 297\u2013328.","journal-title":"Adv. Comput. Math."},{"key":"BF02207699_CR14","unstructured":"J. Illan and G. L\u00f3pez-Lagomasino, A note on generalized quadrature formulas of Gauss-Jacobi type, in:Constructive Theory of Functions '84, Sofia (1984) pp. 513\u2013518."},{"key":"BF02207699_CR15","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1112\/blms\/21.2.113","volume":"21","author":"W. B. Jones","year":"1989","unstructured":"W. B. Jones, O. Nj\u00e5stad and W. J. Thron, Moment theory, orthogonal polynomials, quadrature and continued fractions associated with the unit circle, Bull. London Math. Soc. 21 (1989) 113\u2013152.","journal-title":"Bull. London Math. Soc."},{"key":"BF02207699_CR16","doi-asserted-by":"crossref","first-page":"239","DOI":"10.2307\/2374574","volume":"109","author":"A. M\u00e1t\u00e9","year":"1987","unstructured":"A. M\u00e1t\u00e9, P. Nevai and V. Totik, Strong and weak convergence of orthogonal polynomials, Amer. J. Math. 109 (1987) 239\u2013281.","journal-title":"Amer. J. Math."},{"key":"BF02207699_CR17","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1093\/imamat\/21.2.165","volume":"21","author":"J. Nuttal","year":"1987","unstructured":"J. Nuttal and C. J. Wherry, Gauss integration for complex weight functions, J. Inst. Math. Appl. 21 (1987) 165\u2013170.","journal-title":"J. Inst. Math. Appl."},{"key":"BF02207699_CR18","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1070\/SM1977v032n02ABEH002377","volume":"32","author":"E. A. Rakhmanov","year":"1977","unstructured":"E. A. Rakhmanov, On the asymptotics of the ratio of orthogonal polynomials, Mat. Sb. 32 (1977) 199\u2013213.","journal-title":"Mat. Sb."},{"key":"BF02207699_CR19","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1070\/SM1983v046n01ABEH002749","volume":"46","author":"E. A. Rakhmanov","year":"1983","unstructured":"E. A. Rakhmanov, On the asymptotics of the ratio of orthogonal polynomials II, Mat. Sb. 46 (1983) 105\u2013117.","journal-title":"Mat. Sb."},{"key":"BF02207699_CR20","doi-asserted-by":"crossref","unstructured":"H. Stahl and V. Totik,General Orthogonal Polynomials, Encyclopedia of Mathematics and its Applications (Cambridge University Press, 1992).","DOI":"10.1017\/CBO9780511759420"},{"key":"BF02207699_CR21","volume-title":"Amer. Math. Soc. Colloq. Publ. 33","author":"G. Szeg\u00f3","year":"1967","unstructured":"G. Szeg\u00f3,Orthogonal Polynomials, Amer. Math. Soc. Colloq. Publ. 33 (Amer. Math. Soc., Providence, RI, 3rd ed., 1967; 1st ed., 1939).","edition":"3rd ed."},{"key":"BF02207699_CR22","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1090\/S0025-5718-1993-1195424-6","volume":"16","author":"W. Assche Van","year":"1993","unstructured":"W. Van Assche and I. Vanherwegen, Quadrature formulas based on rational interpolation, Math. Comp. 16 (1993) 765\u2013783.","journal-title":"Math. Comp."},{"key":"BF02207699_CR23","doi-asserted-by":"crossref","unstructured":"H. Wallin, Potential theory and approximation of analytic functions by rational interpolation, in:Complex Analysis, Joensuu 1978, eds. I. Laine, O. Letho and T. Sorvali, Lecture Notes in Mathematics 747 (Springer, 1979) pp. 434\u2013450.","DOI":"10.1007\/BFb0064002"},{"key":"BF02207699_CR24","volume-title":"Amer. Math. Soc. Colloq. Publ. 20","author":"J. L. Walsh","year":"1960","unstructured":"J. L. Walsh,Interpolation and Approximation, Amer. Math. Soc. Colloq. Publ. 20 (Amer. Math. Soc., Providence, RI, 3rd ed., 1960; 1st ed., 1935).","edition":"3rd ed."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02207699.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02207699\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02207699","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,4]],"date-time":"2023-05-04T23:45:18Z","timestamp":1683243918000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02207699"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,2]]},"references-count":24,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1996,2]]}},"alternative-id":["BF02207699"],"URL":"https:\/\/doi.org\/10.1007\/bf02207699","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,2]]}}}