Newton-HSS methods, that are variants of inexact Newton methods different from Newton-Krylov methods, have been shown to be competitive methods for solving large sparse systems of nonlinear equations with positive definite Jacobian matrices [Bai and Guo, 2010]. In that paper, only local convergence was proved. In this paper, we prove a Kantorovich-type semilocal convergence. Then we introduce N...

In this paper, a new scheme of the evaluation of numerical integration by using Centroidal mean derivative based closed Newton cotes quadrature rule (CMDCNC) is presented in which the centroidal mean is used for the computation of function derivative. The accuracy of these numerical formulas are higher than the existing closed Newton cotes quadrature (CNC) fromula. The error terms are also obta...

Image reconstruction gives rise to some challenging large-scale constrained optimization problems. We consider a convex minimization problem with nonnegativity constraints that arises in astronomical imaging. To solve this problem, we use an efficient hybrid gradient projection-reduced Newton (active-set) method. By "reduced Newton," we mean that we take Newton steps only in the inactive variab...