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Potra, F. A.

The rate of convergence of a modified Newton’s process. (English) Zbl 0486.65039

Apl. Mat. 26, 13-17 (1981).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
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Cited in 7 Documents

MSC:

65J15 Numerical solutions to equations with nonlinear operators
47J25 Iterative procedures involving nonlinear operators

Keywords:

method of nondiscrete mathematical induction; rate of convergence; Newton’s process; sharp error bounds

Citations:

Zbl 0304.65037
Cite Review PDF
Full Text: DOI EuDML

References:

[1] M. Frechet: La notion de différentielle dans l’analyse générale. Ann. Ec. Norm. Sup., 42, (1925), 293-323. · JFM 51.0312.03
[2] Л. В. Канторович: Фунциональный анализ и прикладная математика. Y. M. H., 3, 89-185 (1948). · Zbl 1154.94303
[3] Л. В. Канторович: О методе Ньютона. Труды Матем. Института Стеклова, 28, 104-144 (1949). · Zbl 1152.51302
[4] Л. В. Канторович Г. П. Акилов: Фунциональный анализ. Издание второе переработанное, Москва (1977). · Zbl 1225.01071 · doi:10.1126/science.196.4286.144
[5] V. Pták: Nondiscrete mathematical induction and iterative existence proofs. Linear algebra and its applications 13 (1976), 223 - 238. · Zbl 0323.46005 · doi:10.1016/0024-3795(76)90098-7
[6] V. Pták: The rate of convergence of Newton’s process. Num. Math., 25 (I976), 279-285., · Zbl 0304.65037 · doi:10.1007/BF01399416
[7] L. Schwartz: Analyse Mathématique. Herman, Paris, 1967. · Zbl 0171.01301
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