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On the round-off error in the method of successive over-relaxation

Author: M. Stuart Lynn
Journal: Math. Comp. 18 (1964), 36-49
MSC: Primary 65.35; Secondary 65.62
MathSciNet review: 0162364
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Abstract: The asymptotic behavior of the round-off error, which accumulates when the well-known iterative method of (point) successive over-relaxation is used to solve a large-scale system of linear equations, is examined by means of a statistical model. The local round-off errors are treated as independent random variables and expressions for the mean and variance of the accumulated round-off error are obtained, as the number of iterations tends to infinity.

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

  • [1] A. A. Abramov, ``On the influence of round-off errors in the solution of Laplace's equation,'' Vycis. Matem. i Vycis. Teh., v. 1, 1953, p. 37-41. MR 0070267 (16:1156e)
  • [2] J. Descloux, ``Note on the round-off error in iterative processes,'' Math. Comp., v. 17, 1963, p. 18-27. MR 0152102 (27:2082)
  • [3] G. E. Forsythe, ``Note on rounding-off errors,'' SIAM Rev., v. 1, 1959, p. 66-67. MR 0099119 (20:5563)
  • [4] G. H. Golub, ``The use of Chebyshev matrix polynomials in the iterative solution of linear equations compared to the method of successive over-relaxation,'' Doctoral Thesis, University of Illinois, 1959.
  • [5] G. H. Golub, Bounds for the Round-Off Errors in the Richardson Second-Order Method, Nordisk Tidskrift for Informations-Behandlung, v. 2, 1962, p. 212-223. MR 0165678 (29:2958)
  • [6] G. H. Golub, & J. K. Moore, ibid (appendix).
  • [7] P. K. Henrici, Discrete-variable Methods in Ordinary Differential Equations, John Wiley & Sons, Inc., New York, 1961.
  • [8] M. Marcus, ``Basic theorems in matrix theory,'' N.B.S. Appl. Math. Ser. No. 57, 1960. MR 0109824 (22:709)
  • [9] A. Ostrowski, ``On the linear iteration procedures for symmetric matrices,'' Rendic. di Mat. e.d.s. Applicaz, v. 13, 1954, p. 1-24. MR 0070261 (16:1155e)
  • [10] W. Sibagaki, ``On the idea of 'numerical convergence' and its applications,'' Mem. Fac. Sci. Kyushu Univ. Ser. A, v. 5, 1950, p. 89-97. MR 0039364 (12:537f)
  • [11] A. M. Turing, ``Rounding errors in algebraic processes,'' Quart. J. Appl. Math., v. 1, 1948, p. 287-307. MR 0028100 (10:405c)
  • [12] M. Urabe, ``Convergence of numerical iteration in solution of equations,'' J. Sci. Hiroshima Univ. Ser. A, v. 19, 1956, p. 479-489. MR 0092225 (19:1081g)
  • [13] R. S. Varga, Matrix Iterative Analysis, Prentice-Hall, New Jersey, 1962. MR 0158502 (28:1725)
  • [14] J. H. Wilkinson, ``Rounding errors in algebraic processes,'' Proc. Int. Conference on Information Processing, UNESCO, 1959, p. 44. MR 0121976 (22:12703)
  • [15] J. H. Wilkinson, Error analysis of direct methods of matrix inversion,'' J. Assoc. Comp. Mach., v. 8, 1961, p. 281-330. MR 0176602 (31:874)
  • [16] D. M. Young, ``Iterative methods for solving-partial differential equations of the elliptic type,'' Trans. Amer. Math. Soc., v. 76, 1954, p. 92-111. MR 0059635 (15:562b)

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Article copyright: © Copyright 1964 American Mathematical Society

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