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Fast Iterative Division of p-adic Numbers

Krishnamurthy, EV and Murthy, VK (1983) Fast Iterative Division of p-adic Numbers. In: IEEE Transactions on Computers, 32 (4). pp. 396-398.

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A fast iterative scheme based on the Newton method is described for finding the reciprocal of a finite segment p-adic numbers (Hensel code). The rate of generation of the reciprocal digits per step can be made quadratic or higher order by a proper choice of the starting value and the iterating function. The extension of this method to find the inverse transform of the Hensel code of a rational polynomial over a finite field is also indicated.

Item Type: Journal Article
Publication: IEEE Transactions on Computers
Publisher: IEEE
Additional Information: Copyright 1983 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Keywords: Hensel code;Hensel lemma;higher order convergence;iterate; Newton method;p-adic numbers;quadratic convergence;reciprocal.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 19 Jul 2009 09:00
Last Modified: 19 Sep 2010 05:34
URI: http://eprints.iisc.ac.in/id/eprint/20711

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