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

IF 1 4区数学

Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2018-07-12 DOI:10.4236/am.2018.97059

I. Fried

引用次数: 0

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.

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Newton, Halley, Pell和√N的最优迭代高阶有理逼近

本文研究了求解非线性代数方程f (x) = x2 - N = 0的单步迭代方法，得到了在Pell方程p2 - Nq2 = k意义上对整数k最优的有理逼近p/q，交替收敛或相反收敛。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Mathematics-A Journal of Chinese Universities Series B MATHEMATICS, APPLIED-

自引率

10.00%

发文量

期刊介绍： Applied Mathematics promotes the integration of mathematics with other scientific disciplines, expanding its fields of study and promoting the development of relevant interdisciplinary subjects. The journal mainly publishes original research papers that apply mathematical concepts, theories and methods to other subjects such as physics, chemistry, biology, information science, energy, environmental science, economics, and finance. In addition, it also reports the latest developments and trends in which mathematics interacts with other disciplines. Readers include professors and students, professionals in applied mathematics, and engineers at research institutes and in industry. Applied Mathematics - A Journal of Chinese Universities has been an English-language quarterly since 1993. The English edition, abbreviated as Series B, has different contents than this Chinese edition, Series A.