## Solving equations

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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
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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