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Sharp error bounds for Newton's process

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Summary

The method of nondiscrete mathematical induction is applied to the Newton process. The method yields a very simple proof of the convergence and sharp apriori estimates; it also gives aposteriori bounds which are, in general, better than those given in [1].

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Potra, F.A., Pták, V. Sharp error bounds for Newton's process. Numer. Math. 34, 63–72 (1980). https://doi.org/10.1007/BF01463998

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