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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Quadrature formulas with simple Gaussian nodes and multiple fixed nodes
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by D. D. Stancu and A. H. Stroud PDF
Math. Comp. 17 (1963), 384-394 Request permission
References
    E. B. Christoffel, “Über die Gaussische Quadratur und eine Verallgemeinerungderselben,” J. Reine Angew. Math., v. 55, 1858, p. 61-82. J. Deruyts, “Sur le calcul approché de certaines integrales definies,” Bull. de l’Acad. de Belgique, v. 2, 1886, p. 301-311. C. F. Gauss, “Methodus nova integralium valores per approximationen inveniendi,” Werke, v. 3, 1866, p. 163-196. E. Heine, Handbuch der Kugelfunctionen, Vol. 1, Berlin, 1878. C. Hermite, “Sur la formule d’interpolation de Lagrange,” J. Reine Angew. Math., v. 84, 1878, p. 70-79.
  • D. V. Ionescu, Cuadraturi numerice, Academia Republicii Populare Romîne, Ştiinţă şi Tehnică, vol. 10, Editura Tehnică, Bucharest, 1957 (Italian). MR 0130117
  • Vladimir Ivanovich Krylov, Approximate calculation of integrals, The Macmillan Company, New York-London, 1962, 1962. Translated by Arthur H. Stroud. MR 0144464
  • R. Lobatto, Lessen over de Integraal-Rekening, The Hague, 1852.
  • A. Markoff, Sur la méthode de Gauss pour le calcul approché des intégrales, Math. Ann. 25 (1885), no. 3, 427–432 (French). MR 1510316, DOI 10.1007/BF01443287
  • F. G. Mehler, “Bemerkungen zur Theorie der mechanische Quadraturen,” J. Reine Angew. Math., v. 63, 1864, p. 152-157.
  • N. Obreschkoff, Neue Quadraturformeln, Abh. Preuss. Akad. Wiss. Math.-Nat. Kl. 1940 (1940), no. 4, 20 (German). MR 0003867
  • K. Petr, “O jedné formuli pro numerický výpocet určitých integrálu,” Časopis Pěst. Mat. Fys., v. 44, 1915, p. 454-455. K. A. Posse, “Sur les quadratures,” Nouv. Ann. de Math., (2) v. 14, 1875, p. 49-62. R. Radau, “Étude sur les formules d’approximation qui servent à calculer la valeur numérique d’une intégrale définie,” J. Math. Pures Appl., (3) v. 6, 1880, p. 283-336.
  • Harry A. Rothmann, Gaussian quadrature with weight function $x^{n}$ on the interval $(-1,\,1)$, Math. Comp. 15 (1961), 163–168. MR 121991, DOI 10.1090/S0025-5718-1961-0121991-6
  • James B. Scarborough, Numerical Mathematical Analysis, Johns Hopkins Press, Baltimore, Md.; Oxford University Press, London, 1950. 2d ed. MR 0039361
  • D. D. Stancu, La généralisation de la formule de quadrature de Gauss-Christoffel, Acad. R. P. Romîne. Fil. Iaşi. Stud. Cerc. Şti. Mat. 8 (1957), no. 1, 1–18 (Romanian, with Russian and French summaries). MR 0095372
  • D. D. Stancu, Sur la formule d’interpolation d’Hermite et quelques applications de celle-ci, Acad. R. P. Romîne Fil. Cluj Stud. Cerc. Mat. 8 (1957), 339–355 (Romanian, with French and Russian summaries). MR 107368
  • D. D. Stancu, Sur quelques formules générales de quadrature du type Gauss-Christoffel, Mathematica (Cluj) 1(24) (1959), no. 1, 167–182 (French). MR 120323
  • T. J. Stieltjes, Quelques recherches sur la théorie des quadratures dites mécaniques, Ann. Sci. École Norm. Sup. (3) 1 (1884), 409–426 (French). MR 1508747
  • A. H. Stroud, A bibliography on approximate integration, Math. Comput. 15 (1961), 52–80. MR 0116469, DOI 10.1090/S0025-5718-1961-0116469-X
  • A. H. Stroud & D. Secrest, “A multiple precision floating point interpretive program for the Control Data 1604,” Comput. J., v. 6, 1963, p. 62-66. G. Szegö, Orthogonal Polynomials, Amer. Math. Soc. Colloq. Publ., v. 23, 1959, p. 30.
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Additional Information
  • © Copyright 1963 American Mathematical Society
  • Journal: Math. Comp. 17 (1963), 384-394
  • MSC: Primary 65.55
  • DOI: https://doi.org/10.1090/S0025-5718-1963-0157485-3
  • MathSciNet review: 0157485