If Newton's method is employed to find a root of a map from a Banach space into itself and the derivative is singular at that root, linear convergence of the Newton sequence to the root is the best ...

Newton's Method: Newton's Method is a technique for approximating a root to an equation of the form f (x) = 0. What is required is an initial estimate for the root, called x 1, and an iterative ...

We prove the well-posedness of the numerical scheme. Then we show under appropriate nondegeneracy conditions on the paxametrization that Newton's method converges locally and quadratically. Finally, ...