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Mathematics of Computation

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Journal: Math. Comp. 2 (1946), 55-61
DOI: https://doi.org/10.1090/S0025-5718-46-99631-7
Corrigendum: Math. Comp. 2 (1947), 228.
Corrigendum: Math. Comp. 2 (1946), 95-96.
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References | Additional Information

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

  • [1] See E. T. Whittaker & G. Robinson, The Calculus of Observations, third ed., London, 1940.
  • [2] D. H. Lehmer, ``The Graeffe process as applied to power series,'' MTAC, v. 1, p. 377f. MR 0012913 (7:84a)
  • [3] C. Runge & H. König, Vorlesungen über numerisches Rechnen, Berlin, 1924. The method was given earlier in C. Runge, Praxis der Gleichungen (Sammlung Schubert), Leipzig, 1900.
  • [5] S. Brodetsky & G. Smeal, ``On Graeffe's method for complex roots of algebraic equations,'' Camb. Phil. So., Proc., v. 22, 1924, p. 83f.
  • [7] A. Ostrowski, ``Sur la continuité relative des racines d'équations algébriques,'' Académie d. Sci., Paris, Comptes Rendus, v. 209, 1939, p. 777f, has illustrated this very forcibly by comparison of $ {z^4} - 4{z^3} + 6{z^2} - 4z + 1 = 0$, roots 1, 1, 1, 1; with $ {z^4} - 4{z^3} + 5.999951{z^2} - 4z + 1 = 0$, roots 1.0872, .9198, .9965 $ \pm$ .0836i.
  • [8] Shih-nge Lin, ``A method for finding roots of algebraic equations,'' J. Math. Phys., v. 22, 1943, p. 60f. MR 0008709 (5:49f)
  • [1] A. P. Hillman & H. E. Salzer, ``Roots of $ \sin z = z$,'' Phil. Mag., s. 7, v. 34, 1943, p. 575. See MTAC, v. 1, p. 141. MR 0008710 (5:49g)


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DOI: https://doi.org/10.1090/S0025-5718-46-99631-7
Article copyright: © Copyright 1946 American Mathematical Society

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