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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