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…
linear systems in Rn
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)…