## 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…

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

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

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

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

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

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