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 AM  Vol.9 No.7 , July 2018
Newton, Halley, Pell and the Optimal Iterative High-Order Rational Approximation of √N
Abstract:
In this paper we examine single-step iterative methods for the solution of the nonlinear algebraic equation f (x) = x2 - N = 0 , for some integer N, generating rational approximations p/q that are optimal in the sense of Pell’s equation p2 - Nq2 = k for some integer k, converging either alternatingly or oppositely.
Cite this paper: Fried, I. (2018) Newton, Halley, Pell and the Optimal Iterative High-Order Rational Approximation of √N. Applied Mathematics, 9, 861-873. doi: 10.4236/am.2018.97059.
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