Skip to Main Content

Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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.

 

Approximate solutions of Fredholm-type integral equations
HTML articles powered by AMS MathViewer

by A. T. Lonseth PDF
Bull. Amer. Math. Soc. 60 (1954), 415-430
References
    1. I. A. Akbergenov, On the approximate solution of Fredholm’s equation and determination of its characteristic values(Russian), Mat. Sbornik vol. 42 (1935) pp. 679-697; German summary, p. 698. 2. S. Banach, Théorie des opérations linéaires, Warsaw, 1932. 3. H. Bateman, On the numerical solution of linear integral equations, Proc. Roy. Soc. London Ser. A vol. 100 (1922) pp. 441-449.
  • E. Bodewig, Bericht über die verschiedenen Methoden zur Lösung eines Systems linearer Gleichungen mit reellen Koeffizienten. IV, V, Nederl. Akad. Wetensch., Proc. 51 (1948), 53–64, 211–219=Indagationes Math. 10, 24–35, 82–90 (1948) (German). MR 25261
  • E. Bodewig, Konvergenztypen und das Verhalten von Approximationen in der Nähe einer mehrfachen Wurzel einer Gleichung, Z. Angew. Math. Mech. 29 (1949), 44–51 (German, with Russian summary). MR 29266, DOI 10.1002/zamm.19490290133
  • H. Bückner, Die praktische Behandlung von Integral-Gleichungen, Ergebnisse der angewandten Mathematik. Bd. 1, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1952 (German). MR 0049661, DOI 10.1007/978-3-662-01394-6
  • F. B. Hildebrand and P. D. Crout, A least square procedure for solving integral equations by polynomial approximation, J. Math. Phys. Mass. Inst. Tech. 20 (1941), 310–335. MR 5444, DOI 10.1002/sapm1941201310
    • 8. L. Euler, Introductio in analysin infinitorum, vol. 1, Opera Omnia, Ser. 1, vol. 8, Leipzig-Berlin, 1922. 9. L. Euler, Institutiones calculi differential, Opera Omnia, Ser. 1, vol. 10, Leipzig-Berlin, 1913.
  • Ivar Fredholm, Sur une classe d’équations fonctionnelles, Acta Math. 27 (1903), no. 1, 365–390 (French). MR 1554993, DOI 10.1007/BF02421317
  • E. Goursat, Sur un cas élémentaire de l’équation de Fredholm, Bull. Soc. Math. France 35 (1907), 163–173 (French). MR 1504578, DOI 10.24033/bsmf.804
    • 12. E. Hellinger and O. Toeplitz, Integralgleichungen und Gleichungen mit unendlich vielen Unbekannten, Encyklopädie math. Wissenschaften II C 13; U. S. reprint 1953, Chelsea.
  • David Hilbert, Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen, Chelsea Publishing Co., New York, N.Y., 1953 (German). MR 0056184
  • F. B. Hildebrand, Methods of applied mathematics, Prentice-Hall, Inc., New York, N. Y., 1952. MR 0057300
  • L. V. Kantorovich, Functional analysis and applied mathematics, U. S. Department of Commerce, National Bureau of Standards, Los Angeles, Calif., 1952. Translated by C. D. Benster; NBS Rep. 1509. MR 0053389
  • L. V. Kantorovič and V. I. Krylov, Približennye metody vysšego analiza, Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow-Leningrad, 1950 (Russian). 3d ed.]. MR 0042210
    • 17. M. F. Kravchuk (M. Krawtshouk), Application of the method of moments to solution of linear differential and integral equations(Ukrainian), Kiev, 1932. 18. N. M. Krylov, Sur différents procédés d’intégration approchée en physique mathématique, Ann. Fac. Sci. Univ. Toulouse vol. 27 (1925) pp. 153-186; vol. 29 (1927) pp. 167-199.
  • A. T. Lonseth, The propagation of error in linear problems, Trans. Amer. Math. Soc. 62 (1947), 193–212. MR 22315, DOI 10.1090/S0002-9947-1947-0022315-4
  • Arvid T. Lonseth, An extension of an algorithm of Hotelling, Proceedings of the Berkeley Symposium on Mathematical Statistics and Probability, 1945, 1946, University of California Press, Berkeley-Los Angeles, Calif., 1949, pp. 353–357. MR 0029546
  • E. J. Nyström, Über Die Praktische Auflösung von Integralgleichungen mit Anwendungen auf Randwertaufgaben, Acta Math. 54 (1930), no. 1, 185–204 (German). MR 1555306, DOI 10.1007/BF02547521
    • 22. E. N. Oberg, The approximate solution of integral equations, Bull. Amer. Math. Soc. vol. 41 (1935) pp. 276-284. 23. A. Ostrowski, Sur une transformation de la série de Liouville-Neumann, C. R. Acad. Sci. Paris vol. 203 (1936) p. 602. 24. A. Ostrowski, Sur Vapproximation du déterminant de Fredholm par les déterminants des systèmes d’équations linéaires, Arkiv för Matematik, Astronomi och Fysik vol. 26A (1938) pp. 1-15. 25. M. Picone, Sul metodo delle minime potenze ponderate e sul metodo di Ritz per il calcolo approssimato nei problemi della fisica-matematica, Rend. Circ. Mat. Palermo vol. 52 (1928) pp. 225-253.
  • Erhard Schmidt, Zur Theorie der linearen und nicht linearen Integralgleichungen Zweite Abhandlung, Math. Ann. 64 (1907), no. 2, 161–174 (German). MR 1511432, DOI 10.1007/BF01449890
    • 27. F. Tricomi, Sulla risoluzione numerica delle equazioni integrali di Fredholm, Atti della Accademia Nazionale dei Lincei Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali (5) vol. 33 (1924) 1° sem., pp. 483-486, 2° sem., pp. 26-30.
  • Carl Wagner, On the solution of Fredholm integral equations of second kind by iteration, J. Math. Physics 30 (1951), 23–30. MR 0041550, DOI 10.1002/sapm195130123
  • George E. Forsythe, Solving linear algebraic equations can be interesting, Bull. Amer. Math. Soc. 59 (1953), 299–329. MR 56372, DOI 10.1090/S0002-9904-1953-09718-X
Additional Information
  • Journal: Bull. Amer. Math. Soc. 60 (1954), 415-430
  • DOI: https://doi.org/10.1090/S0002-9904-1954-09825-7
  • MathSciNet review: 0064497