In this paper we discuss ellipticity conditions for some parameter-dependent boundary value problems which do not satisfy the Agmon–Agranovich–Vishik condition of ellipticity with parameter. The appropriate definition of ellipticity uses the concept of the Newton polygon. For the corresponding boundary value problems with small parameter we construct the formal asymptotic solution, thus explain...

We present a work in progress aimed at measuring the spectrum of the Cosmic X-ray Background (CXB) with the EPIC detectors onboard XMM-Newton. Our study includes a detailed characterization of the EPIC non X-ray background, which is crucial in making a robust measurement of the spectrum of CXB. We present preliminary results, based on the analysis of a set of Commissioning and Performance Verif...

A new family of limited-memory variationally-derived variable metric or quasi-Newton methods for unconstrained minimization is given. The methods have quadratic termination property and use updates, invariant under linear transformations. Some encouraging numerical experience is reported.

The local superlinear convergence of the generalized Newton method for solving systems of nonsmooth equations has been proved by Qi and Sun under the semismooth condition and nonsingularity of the generalized Jacobian at the solution. Unlike the Newton method for systems of smooth equations, globalization of the generalized Newton method seems dif-cult to achieve in general. However, we show th...

In this work a Newton interior–point method for the solution of Karush– Kuhn–Tucker systems is presented. A crucial feature of this iterative method is the solution, at each iteration, of the inner subproblem. This subproblem is a linear–quadratic programming problem, that can solved approximately by an inner iterative method such as the Hestenes multipliers’ method. A deep analysis on the choi...

Under the hypothesis that the derivative satisfies some kind of weak Lipschitz condition, sharp estimates of the radii of convergence balls of Newton-like methods for operator equations are given in Banach space. New results can be used to analyze the convergence of other developed Newton iterative methods.