Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The numerical solutions of the eigenvalue problem for compact integral operators

Author: Kendall E. Atkinson
Journal: Trans. Amer. Math. Soc. 129 (1967), 458-465
MSC: Primary 47.70; Secondary 65.00
MathSciNet review: 0220105
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] P. M. Anselone, Convergence and error bounds for approximate solutions of integral and operator equations, Error in Digital Computation, Vol. 2 (Proc. Sympos. Math. Res. Center, U .S. Army, Univ. Wisconsin, Madison, Wis., 1965) Wiley, New York, 1965, pp. 231–252. MR 0189277
  • [2] P. M. Anselone and R. H. Moore, Approximate solutions of integral and operator equations, J. Math. Anal. Appl. 9 (1964), 268–277. MR 0184448,
  • [3] K. E. Atkinson, Extensions of the Nyström method for the numerical solution of linear integral equations of the second kind, U.S. Army Math. Research Center Tech. Rep. #686; Ph.D. thesis, Univ. of Wisconsin, Madison, 1966.
  • [4] Helmut Brakhage, Über die numerische Behandlung von Integralgleichungen nach der Quadraturformelmethode, Numer. Math. 2 (1960), 183–196 (German). MR 0129147,
  • [5] Helmut Brakhage, Zur Fehlerabschätzung für die numerische Eigenwertbestimmung bei Integralgleichungen, Numer. Math. 3 (1961), 174–179 (German). MR 0129148,
  • [6] Hans Bückner, Konvergenzuntersuchungen bei einem algebraischen Verfahren zur näherungsweisen Lösung von Integralgleichungen, Math. Nachr. 3 (1950), 358–372 (German). MR 0048926,
  • [7] -, ``Numerical methods for integral equations,'' in Survey of numerical analysis, pp. 439-467, edited by John Todd, McGraw-Hill, New York, 1962.
  • [8] N. Dunford and J. T. Schwartz, Linear operators, Vol. I, Interscience, New York, 1957.
  • [9] L. V. Kantorovich and V. I. Krylov, Approximate methods of higher analysis, Translated from the 3rd Russian edition by C. D. Benster, Interscience Publishers, Inc., New York; P. Noordhoff Ltd., Groningen, 1958. MR 0106537
  • [10] E. J. Nyström, Über Die Praktische Auflösung von Integralgleichungen mit Anwendungen auf Randwertaufgaben, Acta Math. 54 (1930), no. 1, 185–204 (German). MR 1555306,
  • [11] Frigyes Riesz and Béla Sz.-Nagy, Functional analysis, Frederick Ungar Publishing Co., New York, 1955. Translated by Leo F. Boron. MR 0071727
  • [12] Angus E. Taylor, Introduction to functional analysis, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1958. MR 0098966
  • [13] R. E. Turner, Eigenfunction expansions in Banach spaces, U.S. Army Math. Research Center Tech. Rep. #600, Madison, Wisconsin, 1966.
  • [14] Helmut Wielandt, Error bounds for eigenvalues of symmetric integral equations, Proceedings of Symposia in Applied Mathematics. Vol. VI. Numerical analysis, McGraw-Hill Book Company, Inc., New York, for the American Mathematical Society, Providence, R. I., 1956, pp. 261–282. MR 0086402

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 47.70, 65.00

Retrieve articles in all journals with MSC: 47.70, 65.00

Additional Information

Article copyright: © Copyright 1967 American Mathematical Society

American Mathematical Society