Fast Iterative Division of p-adic Numbers

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 funct...

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Bibliographic Details
Published in:IEEE transactions on computers Vol. C-32; no. 4; pp. 396 - 398
Main Authors: KRISHNAMURTHY, E. V, MURTHY, V. K
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.04.1983
Institute of Electrical and Electronics Engineers
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Arithmetic
Circuits and systems
Codes
Computer science; control theory; systems
Convergence
Digital signal processing
Exact sciences and technology
Finite element analysis
Hensel code
Hensel lemma
higher order convergence
iterate
Iterative methods
Laplace equations
Newton method
p-adic numbers
Polynomials
quadratic convergence
reciprocal
Theoretical computing
Computers arithmetic
ISSN:0018-9340, 1557-9956
Online Access:Get full text
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Summary: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.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0018-9340
1557-9956
DOI:10.1109/TC.1983.1676241