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Sharp error bounds for Newton’s process. (English) Zbl 0434.65034

MSC:
65J15 Numerical solutions to equations with nonlinear operators
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References:
[1] Gragg, W.B., Tapia, R.A.: Optimal error bounds for the Newton-Kantorovich theorem. SIAM J., Numer. Anal.11, 10-13 (1974) · Zbl 0284.65042
[2] Kantorovich, L.V.: Functional analysis and applied mathematics. Uspekhi Mat. Nauk.3, 89-185 (1948) (Russian) · Zbl 0034.21203
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[4] Ortega, J.M., Rheinboldt, W.C.: Iterative Solution of Nonlinear Equations in Several Variables. New York. Academic Press 1970 · Zbl 0241.65046
[5] Ostrowski, A.I.: Sur la convergence et l’estimation des erreurs dans quelques proc?d?s de r?solution des ?quations num?riques. Collections of Papers in the Memory of D.A. Grave Moscow pp. 213-234, 1940
[6] Ostrowski, A.M.: La m?thode de Newton dans les espaces de Banach. C.R. Acad. Sci. Paris, Ser. A. 272, pp. 1251-1253, 1971 · Zbl 0228.65041
[7] Ostrowski, A.M.: Solution of Equations in Euclidian and Banach Spaces. New York: Academic Press 1973 · Zbl 0304.65002
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[9] Pt?k, V.: A theorem of the closed graph type. Manuscripta math.13, 109-130 (1974) · Zbl 0286.46008
[10] Pt?k, V.: Nondiscrete mathematical induction and iterative existence proofs. Linear algebra and its applications,13, 223-236 (1976) · Zbl 0323.46005
[11] Pt?k, V.: The rate of convergence of Newton’s process. Numer. Math.25, 279-285 (1976) · Zbl 0304.65037
[12] Pt?k, V.: Nondiscrete mathematical induction. In: General topology and its relations to modern analysis and algebra IV, pp. 166-178, Lecture Notes in Mathematics 609, Berlin-Heidelberg-New York: Springer 1977
[13] Pt?k, V.: What should be a rate of convergence? R.A.I.R.O. Analyse Num?rique11, 279-286 (1977) · Zbl 0378.65031
[14] Tapia, R.A.: The Kantorovich theorem for Newton’s method. Amer. Math. Monthly,78, 389-392 (1971) · Zbl 0215.27404
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