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Hensel construction with an arbitrary degree of convergence

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Abstract

This paper presents a Hensel construction over C which can be lifted with an arbitrarily high degree of convergence. First, we focus our attention on two types of Hensel constructions, namely the one which uses Newton’s method and the parallel Hensel construction. We show a close relationship between the two Hensel constructions. We then extend the former, deriving a new Hensel construction which can be lifted with an arbitrarily high degree of convergence. As a numerical example, we show the Hensel construction with convergence of degree 4.

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Authors and Affiliations

  1. Institute of Mathematics, University of Tsukuba, 305, Tsukuba-shi, Japan

    Takuya Kitamoto

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  1. Takuya Kitamoto
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Work supported in part by Japanese Ministry of Education, Science and Culture under Grants 03558008 and 04245102.

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Kitamoto, T. Hensel construction with an arbitrary degree of convergence. Japan J. Indust. Appl. Math. 13, 203–215 (1996). https://doi.org/10.1007/BF03167243

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  • DOI: https://doi.org/10.1007/BF03167243

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