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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the generalized overrelaxation method for operation equations


Author: W. V. Petryshyn
Journal: Proc. Amer. Math. Soc. 14 (1963), 917-924
MSC: Primary 65.10
MathSciNet review: 0169402
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  • [1] J. Albrecht, Fehlerabschätzungen bei Relaxationsverfahren zur numerischen Auflösung linearen Gleichungssystemen, Numer. Math. (3) 3 (1961), 188-201. MR 0146957 (26:4476)
  • [2] R. I. Arms, L. D. Gates and B. Zondek, A method of block iteration, J. Soc. Indust. Appl. Math. 4 (1956), 220-229. MR 0119405 (22:10167)
  • [3] G. E. Forsythe and W. Wasow, Finite-difference methods for partial differential equations, Wiley, New York, 1960. MR 0130124 (23:B3156)
  • [4] S. P. Frankel, Convergence rates of iterative treatments of partial differential equations, Math. Comp. 4 (1950), 65-75. MR 0046149 (13:692e)
  • [5] B. Friedman, The iterative solution of elliptic difference equations, AEC Research and Development Report NYO-7698, New York University, New York, 1957.
  • [6] A. S. Householder, On the convergence of matrix iterations, J. Assoc. Comput. Mach. 3 (1956), 314-324. MR 0082185 (18:514c)
  • [7] W. Kahan, The rate of convergence of the extrapolated Gauss-Seidel iterations (abstract), J. Assoc. Comput. Mach. 4 (1957), 521-522.
  • [8] H. B. Keller, On some iterative methods for solving elliptic difference equations, Quart. Appl. Math. 16 (1958), 209-226. MR 0117893 (22:8667)
  • [9] S. G. Krein, and O. I. Prozorovskaya, An analogue of Seidel's method for operator equations, Voronez. Gos. Univ., Trudy Sem. Functional. Anal. 5 (1957), 35-38. MR 0095579 (20:2081)
  • [10] W. V. Petryshyn, The generalized overrelaxation method for the approximate solution of operator equations in Hilbert space, J. Soc. Indust. Appl. Math. 10 (1962), 675-690. MR 0165723 (29:3003)
  • [11] S. Schechter, Relaxation methods for linear equations, Comm. Pure Appl. Math. 12 (1959), 313-335. MR 0107361 (21:6086)
  • [12] R. S. Varga, A comparison of the successive overrelaxation method and semiiterative methods using Chebyshev polynomials, J. Soc. Indust. Appl. Math. 5 (1957), 39-46. MR 0090129 (19:772d)
  • [13] D. Young, Iterative methods for solving partial difference equations of elliptic type, Trans. Amer. Math. Soc. 76 (1954), 91-111. MR 0059635 (15:562b)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1963-0169402-2
PII: S 0002-9939(1963)0169402-2
Article copyright: © Copyright 1963 American Mathematical Society