homogeneous polynomial map where the Newton method is used to solve an equivalent system of nonlinear equations. The semi …

It is well known that the conjugate gradient method and a quasi-Newton method, using any well-defined update matrix …-definite Hessian. This equivalence does not hold for any quasi-Newton method. We define precisely the conditions on the update matrix … in the quasi-Newton method that give rise to this behavior. We show that the crucial facts are, that the range of each …