## 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…

## Estimating the radius of an attraction ball

Abstract Given a nonlinear mapping $$G:D\subseteq \mathbb{R}^n\rightarrow \mathbb{R}^n$$ differentiable at a fixed point $$x^\ast$$, the Ostrowski theorem offers the sharp…

## On the convergence of some quasi-Newton iterates studied by I. Păvăloiu

Abstract In 1986, I. Păvăloiu [6] has considered a Banach space and the fixed point problem \[x=\lambda D\left( x\right) +y,…

## 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,…

## Affine invariant conditions for the inexact perturbed Newton method

Abstract The high q-convergence orders of the inexact Newton iterates were characterized by Ypma in terms of some affine invariant…

## 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 accelerating the convergence of the successive approximations method

Abstract No q-superlinear convergence to a fixed point $$x^\ast$$ of a nonlinear mapping $$G$$ may be attained by the successive approximations when…

## A note on the quadratic convergence of the inexact Newton methods

Abstract We show that a new sufficient condition for the convergence with q-order two of the inexact Newton iterates may be…

## 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)…

## A note on inexact secant methods

Abstract The inexact secant method $$[x_{k-1},x_{k};F]s_{k}=-F(x_k) +r_k$$, $$x_{k+1}=x_k+s_k$$, $$k=1,2,\ldots$$, $$x_0,x_1 \in {\mathbb R}^n$$ is considered for solving the nonlinear…