Newton method

On the Bounding of the Error in Approximating the Roots of an Equation by Linear or Quadratic Interpolation

1 month ago

Abstract AuthorsTiberiu Popoviciu Institutul de Calcul Keywords? Paper coordinates T. Popoviciu, Sur la délimitation de l’erreur dans l’approximation des racines d’une équation…

Accurate Chebfun solutions to third-order nonlinear BVPs on the half-line. Applications in boundary layer theory

7 months ago

Abstract The paper is devoted to obtaining accurate numerical solutions to some third-order nonlinear boundary problems on the real semi-axis…

How many steps still left to x*?

4 years ago

We survey the convergence orders of sequences and show the orders of the basic iterative sequences for solving nonlinear equations…

Methods of Newton and Newton-Krylov type

5 years ago

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

On an Aitken-Steffensen-Newton type method

7 years ago

Abstract We consider an Aitken-Steffensen type method in which the nodes are controlled by Newton and two-step Newton iterations. We…

The numerical approximation to positive solution for some reaction-diffusion problems

7 years ago

Abstract A one-dimensional reaction-diffusion problem, with the reaction term of the form \(u^{p}\), \(p>1\) is considered. For \(p=3\), we deduce…

Estimating the radius of an attraction ball

8 years ago

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

8 years ago

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

8 years ago

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

8 years ago

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

Newton method

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