Newton's method for finding a zero of a vectorial function is a powerful theoretical and practical tool. One of the drawbacks of the classical convergence proof is that closeness to a non-singularâ€¦ (More)

The Gaussâ€“Newton method for solving nonlinear least squares problems is studied in this paper. Under the hypothesis that the derivative of the function associated with the least square problemâ€¦ (More)

We prove that under semi-local assumptions, the inexact Newton method with a fixed relative residual error tolerance converges Q-linearly to a zero of the non-linear operator under consideration.â€¦ (More)

In this paper some concepts of convex analysis are extended in an intrinsic way from the Euclidean space to the sphere. In particular, relations between convex sets in the sphere and pointed convexâ€¦ (More)

Local convergence analysis of the proximal point method for special class of nonconvex function on Hadamard manifold is presented in this paper. The well definedness of the sequence generated by theâ€¦ (More)

The problem of finding singularities of monotone vectors fields on Hadamard manifolds will be considered and solved by extending the well-known proximal point algorithm. For monotone vector fieldsâ€¦ (More)

We prove Kantorovichâ€™s theorem on Newtonâ€™s method using a convergence analysis which makes clear, with respect to Newtonâ€™s Method, the relationship of the majorant function and the non-linearâ€¦ (More)