Local convergence of a Newton-Traub composition in Banach spaces

DOI10.1007/S40324-017-0113-5zbMath1388.49028OpenAlexW2588315719MaRDI QIDQ1742857

Janak Raj Sharma, Ioannis K. Argyros

Publication date: 12 April 2018

Published in: S\(\vec{\text{e}}\)MA Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40324-017-0113-5

zbMATH Keywords

Banach spacelocal convergenceFréchet-derivativegeneralized Lipschitz-Hölder-type conditionsNewton-Traub method

Mathematics Subject Classification ID

Newton-type methods (49M15) Numerical computation of solutions to systems of equations (65H10) Iterative procedures involving nonlinear operators (47J25) Fréchet and Gateaux differentiability in optimization (49J50)

Related Items (10)

Extending the applicability and convergence domain of a higher-order iterative algorithm under \(\omega\) condition ⋮ On the local convergence of Weerakoon-Fernando method with \(\omega\) continuity condition in Banach spaces ⋮ Extending the applicability of a third-order scheme with Lipschitz and Hölder continuous derivative in Banach spaces ⋮ Extending the applicability of a Newton-Simpson-like method ⋮ About the existence and uniqueness of solutions for some second-order nonlinear BVPs ⋮ Extending the convergence domain of deformed Halley method under \(\omega\) condition in Banach spaces ⋮ On the complexity of extending the convergence ball of Wang's method for finding a zero of a derivative ⋮ Convergence of Traub's iteration under \(\omega\) continuity condition in Banach spaces ⋮ Ball Convergence of Modified Homeier-Like's Method in Banach Spaces under Weak Continuity Condition ⋮ On the convergence of harmonic mean Newton method under \(\omega\) continuity condition in Banach spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• An improvement of Chebyshev-Halley methods free from second derivative
• Means based modifications of Newton's method for solving nonlinear equations
• On the semilocal convergence of a three steps Newton-type iterative process under mild convergence conditions
• Ball convergence theorems and the convergence planes of an iterative method for nonlinear equations
• On the local convergence of a fifth-order iterative method in Banach spaces
• Recurrence relations for rational cubic methods. I: The Halley method
• On some computational orders of convergence
• A third-order modification of Newton method for systems of non-linear equations
• A class of Newton's methods with third-order convergence
• New variants of Jarratt's method with sixth-order convergence
• An improved Newton-Traub composition for solving systems of nonlinear equations
• On Newton-type methods with cubic convergence
• Some new variants of Newton's method.
• Dynamics of the King and Jarratt iterations
• An efficient fourth order weighted-Newton method for systems of nonlinear equations
• Chaotic dynamics of a third-order Newton-type method
• Recurrence relations for a Newton-like method in Banach spaces
• Third-order modification of Newton's method
• A modified Chebyshev's iterative method with at least sixth order of convergence
• Variants of Newton's method using fifth-order quadrature formulas
• Some improvements of Jarratt's method with sixth-order convergence
• New iterations of \(R\)-order four with reduced computational cost
• Geometric mean Newton's method for simple and multiple roots
• A sixth order method for nonlinear equations
• Convergence and Applications of Newton-type Iterations
• A sixth-order family of methods for nonlinear equations
• Some Fourth Order Multipoint Iterative Methods for Solving Equations
• A variant of Newton's method with accelerated third-order convergence
• Chebyshev's approximation algorithms and applications

This page was built for publication: Local convergence of a Newton-Traub composition in Banach spaces