Householder's method for solving the \(p\)-adic polynomial equations
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DOI:
https://doi.org/10.26637/mjm1001/003Abstract
This work offers an analogue of Householder's Method for solving a root-finding problem \(f(x)=0\) in the \(p\)-adic setting. We apply this method to calculate the square roots of a \(p\)-adic number \(a\in\mathbb{Q}_{p}\) where \(p\) is a prime number, and through the calculation of the approached solution of the \(p\)-adic polynomial equation \(f(x)=x^{2}-a=0\). We establish the rate of convergence of this method. Finally, we also determine how many iterations are needed to obtain a specified number of correct digits in the approximate.
Keywords:
\(p\)-adic number, square roots, Householder iterative method, Hensel's lemma,, rate of convergenceMathematics Subject Classification:
26E30, 11E95, 65H04- Pages: 36-46
- Date Published: 01-01-2022
- Vol. 10 No. 01 (2022): Malaya Journal of Matematik (MJM)
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Copyright (c) 2022 Kecies Mohamed
This work is licensed under a Creative Commons Attribution 4.0 International License.
