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      XXV.—On Bernoulli's Numerical Solution of Algebraic Equations

      Proceedings of the Royal Society of Edinburgh

      Cambridge University Press (CUP)

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          Abstract

          The aim of the present paper is to extend Daniel Bernoulli's method of approximating to the numerically greatest root of an algebraic equation. On the basis of the extension here given it now becomes possible to make Bernoulli's method a means of evaluating not merely the greatest root, but all the roots of an equation, whether real, complex, or repeated, by an arithmetical process well adapted to mechanical computation, and without any preliminary determination of the nature or position of the roots. In particular, the evaluation of complex roots is extremely simple, whatever the number of pairs of such roots. There is also a way of deriving from a sequence of approximations to a root successive sequences of ever-increasing rapidity of convergence.

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          Author and article information

          Journal
          applab
          Proceedings of the Royal Society of Edinburgh
          Proc. R. Soc. Edinb.
          Cambridge University Press (CUP)
          0370-1646
          1927
          September 2014
          : 46
          :
          : 289-305
          Article
          10.1017/S0370164600022070
          © 1927

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