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-Fundamentals: Numerical methods

3.3 Newton method

This algorithm can be used for functions for which the derivative f'(x) = df/dx can be evaluated analytically. In this case this method is considerably faster than the half interval.


  • Choose a starting value xi (xoin the graph here below)


  • Calculate the tangent value f'(xi)


  • The condition is that y = f(xi) + f'(xi) (x - xi) = 0


  • from which it can be calculated the new value for the iteration:

    xi+1 = xi - f(xi)/f'(xi)


representation of Newton's algorithm