## On the nonmonotone behavior of the Newton‐GMBACK method

AbstractGMBACK is a Krylov solver for large linear systems, which is based on backward error minimization properties. The minimum backward…

## Methods of Newton and Newton-Krylov type

Book summaryLocal convergence results on Newton-type methods for nonlinear systems of equations are studied. Solving of large linear systems by…

## On the convergence of the Newton-GMBACK method

AbstractWhen the GMBACK solver is used in the Newton iterates, the iterates may be written either as inexact Newton iterates…

## The inexact, inexact perturbed and quasi-Newton methods are equivalent models

Abstract A classical model of Newton iterations which takes into account some error terms is given by the quasi-Newton method,…

## On the superlinear convergence of the successive approximations method

Abstract The Ostrowski theorem is a classical result which ensures the attraction of all the successive approximations xk+1 = G(xk) near a fixed…

## Inexact perturbed Newton methods and applications to a class of Krylov solvers

Abstract Inexact Newton methods are variant of the Newton method in which each step satisfies only approximately the linear system…

## On the high convergence orders of the Newton-GMBACK methods

Abstract GMBACK is a Krylov solver for linear systems in $$\mathbb{R}^n$$. We analyze here the high convergence orders (superlinear convergence)…