On a general iterative method for the approximate solution of linear operator equations
HTML articles powered by AMS MathViewer
- by W. V. Petryshyn PDF
- Math. Comp. 17 (1963), 1-10 Request permission
References
- Horst Bialy, Iterative Behandlung linearer Funktionalgleichungen, Arch. Rational Mech. Anal. 4 (1959), 166–176 (1959) (German). MR 110215, DOI 10.1007/BF00281385
- Hans Bückner, A special method of successive approximations for Fredholm integral equations, Duke Math. J. 15 (1948), 197–206. MR 25290
- Hans Bückner, Ein unbeschränkt anwendbares Iterationsverfahren für Fredholmsche Integralgleichungen, Math. Nachr. 2 (1949), 304–313 (German). MR 35387, DOI 10.1002/mana.19490020506 L. Cesari, “Sulla risoluzione dei sistemi di equazioni lineari per approssimazioni successive,” Atti Accad. Naz. Lincei, Rend. Cl. Sci. Fiz. Mat. Natur. VI. S. 25, 1937, p. 422-428. R. Courant & D. Hilbert, “Methoden der mathematischen Physik,” 2 ed. v. 1, Berlin, Springer, 1931.
- T. Frey, Über ein neues Iterationsverfahren zur Lösung von Integral- und Integrodifferentialgleichungen, Symposium on the numerical treatment of ordinary differential equations, integral and integro-differential equations (Rome, 1960) Birkhäuser, Basel, 1960, pp. 384–387 (German). MR 0129570
- V. M. Fridman, Method of successive approximations for a Fredholm integral equation of the 1st kind, Uspehi Mat. Nauk (N.S.) 11 (1956), no. 1(67), 233–234 (Russian). MR 0076183
- Herbert B. Keller, Special block iterations with applications to Laplace and biharmonic difference equations, SIAM Rev. 2 (1960), 277–287. MR 143347, DOI 10.1137/1002060 H. B. Keller, Numerical methods. Lecture Notes, New York Univ., 1961. R. von Mises & U. H. Pollaczek-Geiringer. “Practische Vorfahren der Gleichungsauflösung,” Z. Angew. Math. Mech., 9, 1929, p. 58-77 and 152-164. W. V. Petryshyn, “The generalized overrelaxation method for the approximate solution of linear operator equations in Hilbert space,” (to be published in SIAM J.).
- W. Quade, Auflösung linearer Gleichungen durch Matrizeniteration, Ber. Math.-Tagung Tübingen 1946 (1947), 123–124 (German). MR 21723
- L. B. Rall, Error bounds for iterative solutions of Fredholm integral equations, Pacific J. Math. 5 (1955), 977–986. MR 79341
- Paul A. Samuelson, Rapidly converging solutions to integral equations, J. Math. Physics 31 (1953), 276–286. MR 0051592
- Mario Schönberg, Sur la méthode d’itération de Wiarda et Bückner pour la résolution de l’équation de Fredholm. II, Acad. Roy. Belgique. Bull. Cl. Sci. (5) 38 (1952), 154–167 (French). MR 0047913
- Angus E. Taylor, Introduction to functional analysis, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1958. MR 0098966
- Carl Wagner, On the solution of Fredholm integral equations of second kind by iteration, J. Math. Physics 30 (1951), 23–30. MR 0041550 G. Wiarda, Integralgleichungen unter besonderer Berücksichtigung der Anwendungen, Leipzig, 1930.
- David Young, Iterative methods for solving partial difference equations of elliptic type, Trans. Amer. Math. Soc. 76 (1954), 92–111. MR 59635, DOI 10.1090/S0002-9947-1954-0059635-7
Additional Information
- © Copyright 1963 American Mathematical Society
- Journal: Math. Comp. 17 (1963), 1-10
- MSC: Primary 65.10
- DOI: https://doi.org/10.1090/S0025-5718-1963-0163426-5
- MathSciNet review: 0163426