 For approximations of the 2nd derivatives (collected in the Hessian matrix), the number of function evaluations is in the order of N².Newton's method requires the 2nd order derivatives, so for each iteration, the number of function calls is in the order of N², but for a simpler pure gradient optimizer it is only N. However, gradient optimizers need usually more iterations than Newton's algorithm.Which one is best with respect to the number of function calls depends on the problem itself.