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Convergence on the iteration of Halley family in weak conditions. (English) Zbl 0884.30004
The author obtains the convergence theorems of the iteration of Hally family in weak conditions by the point estimate.

MSC:
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
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[1] Wang Xinghua, Zheng Shiming, Han Danfu, Convergence on Euler series, The iterations of Euler’s and Halley’s families,Acta Mathematica Sinica, 1990, 33(6): 721. · Zbl 0731.65047
[2] Wang Xinghua, A summary on continuous complexity theory,Contemporary Mathematics, 1994, 163: 155. · Zbl 0809.65055
[3] Smale, S., Newton’s method estimates from data at one point, inThe Merging of Disciplines: New Directions in Pure, Applied and Computational Mathematics (eds. Ewing, R.et al.), New York: Springer-Verlag, 1986, 185–196.
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[6] Wang Xinghua, Convergence of an iterative procedure,Kexue Tongbao, 1975, 20(12): 558.
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[8] Wang Xinghua, Han Danfu, On the dominating sequence method in the point estimates and Smale’s theorem,Science in China, Ser. A, 1990, 33(2): 135. · Zbl 0699.65046
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