Final answer:
Newton's method for optimization converges quadratically, which makes it highly efficient for finding precise solutions provided the initial guess is close to the true solution.
Step-by-step explanation:
The rate of convergence of Newton's method for optimization is quadratic. This means that, given a good initial approximation, the method doubles the number of correct digits of the solution with each iteration. This rapid convergence makes Newton's method very efficient for finding precise solutions to optimization problems when the second derivatives, used to form the Hessian matrix in optimization problems, are continuous and the initial guess is sufficiently close to the true solution.