Abstract
This paper presents a unified derivation of the error bounds in Newton’s process, obtained by Dennis [1], Tapia [10], Gragg-Tapia [3] and recently Potra-Pták [7]. The argument is based upon the Kantorovich theorem and the Kantorovich recurrence relations. In the course of the proof, the relations among their bounds are clarified.
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References
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Yamamoto, T. Error bounds for Newton’s process derived from the Kantorovich theorem. Japan J. Appl. Math. 2, 285–292 (1985). https://doi.org/10.1007/BF03167078
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DOI: https://doi.org/10.1007/BF03167078