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https://doi.org/10.2307/3619622

has been cited by the following article:

• TITLE: Newton, Halley, Pell and the Optimal Iterative High-Order Rational Approximation of √N

  AUTHORS: Isaac Fried

  KEYWORDS: Iterative Methods, Super-Linear and Super-Quadratic Methods, Square Roots, Pell’s Equation, Optimal Rational Iterants, Root Bounds

  JOURNAL NAME: Applied Mathematics, Vol.9 No.7, July 30, 2018

  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.