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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

Automatic Computing Machinery


Journal: Math. Comp. 5 (1951), 232-245
DOI: https://doi.org/10.1090/S0025-5718-51-99416-1
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References | Additional Information

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

  • [1] See, for example, Hilda Geiringer, ``On the solution of systems of linear equations by certain iteration methods,'' Reissner Anniversary Volume, Contributions to Applied Mechanics, Ann Arbor, 1948, p. 365-393. MR 0029272 (10:574e)
  • [2] This is Seidel's result. For a recent proof see R. von Mises & Hilda Geiringer, ``Praktische Verfahren der Gleichungsauflösung,'' Zeitschr. f. angew. Math. u. Mech., v. 9, 1929, p. 58-77, 152-164.
  • [3] See, for example, p. 1044 in John von Neumann & H. H. Goldstine, ``Numerical inverting of matrices of high order,'' Amer. Math. Soc., Bull., v. 53, 1947, p. 1021-1099. MR 0024235 (9:471b)
  • [4] P. Stein, ``Some general theorems on iterates,'' to appear in NBS Jn. of Res.
  • [5] A different proof of this result is given by E. Reich, ``On the convergence of the classical methods of solving linear simultaneous equations,'' Ann. Math. Stat., v. 20, 1949, p. 448-151.


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DOI: https://doi.org/10.1090/S0025-5718-51-99416-1
Article copyright: © Copyright 1951 American Mathematical Society

American Mathematical Society