Summary
This paper gives a method for finding sharpa posteriori error bounds for Newton's method under the assumptions of Kantorovich's theorem. On the basis of this method, new error bounds are derived, and comparison is made among the known bounds of Dennis [2], Döring [4], Gragg-Tapia [5], Kantorovich [6, 7], Kornstaedt [9], Lancaster [10], Miel [11–13], Moret [14], Ostrowski [17, 18], Potra [19], and Potra-Pták [20].
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This paper was written while the author was visiting the Mathematics Research Center, University of Wisconsin-Madison, U.S.A. from March 29, 1985 to October 21, 1985
Sponsored by the Ministry of Education in Japan and the United States Army under Contract No. DAAG 29-80-C-0041
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Yamamoto, T. A method for finding sharp error bounds for Newton's method under the Kantorovich assumptions. Numer. Math. 49, 203–220 (1986). https://doi.org/10.1007/BF01389624
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DOI: https://doi.org/10.1007/BF01389624