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Mathematics of Computation

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

 
 

 

Notes


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?)

    See E. T. Whittaker & G. Robinson, The Calculus of Observations, third ed., London, 1940.
  • D. H. Lehmer, The Graeffe process as applied to power series, Math. Tables Aids Comput. 1 (1945), 377–383. MR 12913, DOI https://doi.org/10.1090/S0025-5718-1945-0012913-8
  • 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. S. Brodetsky & G. Smeal, “On Graeffe’s method for complex roots of algebraic equations,” Camb. Phil. So., Proc., v. 22, 1924, p. 83f. 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.
  • Shih-nge Lin, A method for finding roots of algebraic equations, J. Math. Phys. Mass. Inst. Tech. 22 (1943), 60–77. MR 8709, DOI https://doi.org/10.1002/sapm194322160
  • A. P. Hillman and H. E. Salzer, Roots of $\sin z=z$, Philos. Mag. (7) 34 (1943), 575. MR 8710


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Article copyright: © Copyright 1946 American Mathematical Society