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Fast Iterative Division of p-adic Numbers
April 1983 (vol. 32 no. 4)
pp. 396-398
E.V. Krishnamurthy, Department of Applied Mathematics, Indian Institute of Science, Bangalore 560012, India, and the IDL?Nitro Nobel Basic Research Institute
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.
Index Terms:
reciprocal, Hensel code, Hensel lemma, higher order convergence, iterate, Newton method, p-adic numbers, quadratic convergence
E.V. Krishnamurthy, V.K. Murthy, "Fast Iterative Division of p-adic Numbers," IEEE Transactions on Computers, vol. 32, no. 4, pp. 396-398, April 1983, doi:10.1109/TC.1983.1676241
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