nonlinear systems in Rn Archives | Tiberiu Popoviciu Institute of Numerical Analysis

A survey on the high convergence orders and computational convergence orders of sequences

October 11, 2018

(survey), convergence orders, history, iterative methods, local convergence, nonlinear equations in Banach spaces, nonlinear equations in R, nonlinear systems in Rn, Numerical Analysis, paper, successive approximations

2019

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Abstract The convergence orders (convergence rates) of convergent sequences toward their limit are fundamental notions from Mathematical Analysis and Numerical…

Estimating the radius of an attraction ball

February 10, 2018

Emil Cătinaş

(original), fixed point theory, inexact/perturbed iterations, iterative methods, local convergence, Newton method, nonlinear systems in Rn, Numerical Analysis, paper, successive approximations

2009

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

February 10, 2018

Emil Cătinaş

(original), fixed point theory, iterative methods, local convergence, Newton method, nonlinear equations in Banach spaces, nonlinear systems in Rn, Numerical Analysis, paper, successive approximations

2015

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

February 10, 2018

Emil Cătinaş

(original), inexact/perturbed iterations, iterative methods, Krylov methods, linear systems in Rn, local convergence, Newton method, nonlinear systems in Rn, Numerical Analysis, paper

2005

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

February 10, 2018

Emil Cătinaş

(original), inexact/perturbed iterations, iterative methods, local convergence, Newton method, nonlinear systems in Rn, Numerical Analysis, paper

2002

Abstract The high 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

February 10, 2018

Emil Cătinaş

(original), inexact/perturbed iterations, iterative methods, Krylov methods, linear systems in Rn, local convergence, Newton method, nonlinear systems in Rn, Numerical Analysis, paper

2001

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

February 10, 2018

Emil Cătinaş

(original), fixed point theory, inexact/perturbed iterations, iterative methods, local convergence, nonlinear systems in Rn, Numerical Analysis, paper, successive approximations

2001

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

February 10, 2018

Emil Cătinaş

(original), inexact/perturbed iterations, iterative methods, local convergence, Newton method, nonlinear systems in Rn, Numerical Analysis, paper

2000

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

February 10, 2018

Emil Cătinaş

inexact/perturbed iterations, iterative methods, Krylov methods, linear systems in Rn, local convergence, Newton method, nonlinear systems in Rn, Numerical Analysis, paper

1999

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

A note on inexact secant methods

December 25, 2017

Emil Cătinaş

(original), chord/secant method, inexact/perturbed iterations, iterative methods, local convergence, nonlinear systems in Rn, Numerical Analysis, paper

1996

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