The performance of the secant method in the field of \(p\)-adic numbers

Kecies Mohamed

doi:10.26637/mjm0902/004

Abstract

In this paper, we compute the square roots of \(p\)-adic numbers in \(\mathbb{Q}_{p}\), using the secant method. We also study the performance of this method: the speed of its convergence and the number of iterations necessary to obtain the desired precision \(M\) which represents the number of \(p\)-adic digits in the development of \(\sqrt{a}\).

Keywords:

\(p\)-adic numbers, square roots, secant method, Hensel's lemma, speed of convergence

Mathematics Subject Classification:

26E30, 11E95, 34K28

Authors Imprint References Funding Related Articles Downloads

Kecies Mohamed Laboratoire LMPEA, Université de Jijel, Jijel, Algeria.

Pages: 28-38
Date Published: 01-04-2021
Vol. 9 No. 02 (2021): Malaya Journal of Matematik (MJM)

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