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Solving equations

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  • scolnik
    To solve a nonlinear equation is not in most cases an extremely difficult problem because besides the old reasonable Newton´s method, there are globally
    Message 1 of 1 , Aug 1, 2001
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      To solve a nonlinear equation is not in most cases an extremely difficult
      problem because besides the old reasonable Newton´s method, there are
      globally convergent algorithms using trust regions, etc. In particular
      Richard Brent developed methods whose order of convergence can be
      arbitrarily high (e.g. 6 or 8). Another interesting algorithm is Jarrat´s of
      order 4, which serves as a counterexample of the conjecture that in order to
      get order of convergence m it was necessary to compute m function or
      derivative values (Newton´s uses 2 evaluations for getting order 2 but
      Jarrat´s uses 3 for obtaining order 4). For the sake of simplicity I am not
      here considering the case in which f '(x*) = 0, x* being a zero of the
      function.

      The whole problem is what to solve. In this sense what I read about cracking
      RSA looks far away from a practical approach.

      Cheers

      Hugo Scolnik

      The majority of the time, the thing that gets in the way of success... is your brain


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