Iterative Methods, Including Starting Procedure

  • A. J. Moakes
Chapter
Part of the Introductory Monographs in Mathematics book series (INMOMA)

Abstract

To find the square root of a number N to any required degree of accuracy, starting with a reasonable first approximation x0. Calculate in turn the numbers \({{x}_{1}}=\tfrac{1}{2}\left( {{{x}_{0}}+N/{{x}_{0}}} \right)\); \({{x}_{2}}=\tfrac{1}{2}\left( {{{x}_{1}}+N/{{x}_{1}}} \right)\) and so on, the general relation being \({{x}_{{n+1}}}=\tfrac{1}{2}\left( {{{x}_{n}}+N/{{x}_{n}}} \right)\).

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Copyright information

© A. J. Moakes 1963

Authors and Affiliations

  • A. J. Moakes
    • 1
  1. 1.St. Paul’s SchoolUSA

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