Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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.

 

Direct and iterative methods for the solution of linear operator equations in Hilbert space
HTML articles powered by AMS MathViewer

by W. V. Petryshyn PDF
Trans. Amer. Math. Soc. 105 (1962), 136-175 Request permission
References
  • M. Altman, A simple practical method and a compact computing scheme for the solution of linear equations in Hilbert space, Bull. Acad. Polon. Sci. Cl. III. 5 (1957), 29–33, IV (1 plate) (English, with Russian summary). MR 0085446
  • Felix E. Browder, Functional analysis and partial differential equations. I, Math. Ann. 138 (1959), 55–79. MR 107818, DOI 10.1007/BF01369666
  • R. Courant and D. Hilbert, Methoden der Mathematischen Physik, 2nd Ed., Springer, Berlin, 1931. K. Friedrichs, Spektraltheorie halbbeschränkter Operatoren, Math. Ann. 109 (1934) 465-487, 685-713.
  • Werner Greub and Werner Rheinboldt, On a generalization of an inequality of L. V. Kantorovich, Proc. Amer. Math. Soc. 10 (1959), 407–415. MR 105028, DOI 10.1090/S0002-9939-1959-0105028-3
  • R. M. Hayes, Iterative methods of solving linear problems on Hilbert space, Contributions to the solution of systems of linear equations and the determination of eigenvalues, National Bureau of Standards Applied Mathematics Series, No. 39, U.S. Government Printing Office, Washington, D.C., 1954, pp. 71–103. MR 0066563
  • L. V. Kantorovič, Functional analysis and applied mathematics, Uspehi Matem. Nauk (N.S.) 3 (1948), no. 6(28), 89–185 (Russian). MR 0027947
  • L. V. Kantorovič, Approximate solution of functional equations, Uspehi Mat. Nauk (N.S.) 11 (1956), no. 6(72), 99–116 (Russian). MR 0083696
  • M. V. Keldysh, On the method of Galerkin for the solution of boundary-value problems, Izv. Akad. Nauk SSSR Ser. Mat. 6 (1942), 307-330. M. A. Krasnoselsky and S. G. Krein, Iterative method with minimal residuals, Mat. Sb. 31 (73) (1952), 315-334. M. Kravchuk, Application of the method of moments to the solution of linear differential and integral equations, Ukrain. Akad. Nauk, Kiev (1932). N. M. Krilov, Les méthodes de solution approchée des problems de la physique mathématique, Coll. Mem. de Math., No 49 (1931), Paris.
  • A. D. Lyaško, The convergence of Galerkin type methods, Dokl. Akad. Nauk SSSR 120 (1958), 242–244 (Russian). MR 0097882
  • P. D. Lax and A. N. Milgram, Parabolic equations, Contributions to the theory of partial differential equations, Annals of Mathematics Studies, no. 33, Princeton University Press, Princeton, N.J., 1954, pp. 167–190. MR 0067317
  • A. E. Martynjuk, On a generalization of a variational method, Dokl. Akad. Nauk SSSR (N.S.) 117 (1957), 374–377 (Russian). MR 0108725
  • S. G. Mikhlin, Direct methods in mathematical physics, Moskva-Leningrad, 1950.
  • S. G. Mihlin, On Ritz’s method, Dokl. Akad. Nauk SSSR (N.S.) 106 (1956), 391–394 (Russian). MR 0076314
  • F. J. Murray, The solution of linear operator equations, J. Math. Phys. Mass. Inst. Tech. 22 (1943), 148–157. MR 9091, DOI 10.1002/sapm1943221148
  • N. I. Pol′skiĭ, On the convergence of certain approximate methods of analysis, Ukrain. Mat. Ž. 7 (1955), 56–70 (Russian). MR 0070978
  • William T. Reid, Symmetrizable completely continuous linear transformations in Hilbert space, Duke Math. J. 18 (1951), 41–56. MR 45314
  • Frigyes Riesz and Béla Sz.-Nagy, Functional analysis, Frederick Ungar Publishing Co., New York, 1955. Translated by Leo F. Boron. MR 0071727
  • G. A. Ždanov, On the convergence of a modification of Galerkin’s method, Dokl. Akad. Nauk SSSR (N.S.) 115 (1957), 223–225 (Russian). MR 0109954
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 65.35
  • Retrieve articles in all journals with MSC: 65.35
Additional Information
  • © Copyright 1962 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 105 (1962), 136-175
  • MSC: Primary 65.35
  • DOI: https://doi.org/10.1090/S0002-9947-1962-0145651-8
  • MathSciNet review: 0145651