On the local convergence of Weerakoon-Fernando method with \(\omega\) continuity condition in Banach spaces

DOI10.1007/S40324-020-00217-YOpenAlexW3012911941MaRDI QIDQ827621

Debasis Sharma, Ioannis K. Argyros, Sanjaya Kumar Parhi

Publication date: 13 January 2021

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

Full work available at URL: https://doi.org/10.1007/s40324-020-00217-y

zbMATH Keywords

basin of attractionBanach spacelocal convergence\(\omega\) continuity conditionWeerakoon-Fernando method

Mathematics Subject Classification ID

Newton-type methods (49M15) Iterative procedures involving nonlinear operators (47J25) Numerical solutions to equations with nonlinear operators (65J15) Numerical approximation and computational geometry (primarily algorithms) (65D99)

Related Items (10)

Extending the applicability and convergence domain of a higher-order iterative algorithm under \(\omega\) condition ⋮ A study on the local convergence and complex dynamics of Kou's family of iterative methods ⋮ Local convergence of an optimal method of order four for solving non-linear system ⋮ Extending the applicability of a Newton-Simpson-like method ⋮ Local convergence and complex dynamics of a uni-parametric family of iterative schemes ⋮ Gauss-Newton-Kurchatov method for the solution of non-linear least-square problems using \(\omega\)-condition ⋮ Extending the convergence domain of deformed Halley method under \(\omega\) condition in Banach spaces ⋮ Convergence of Traub's iteration under \(\omega\) continuity condition in Banach spaces ⋮ On the convergence of harmonic mean Newton method under \(\omega\) continuity condition in Banach spaces ⋮ Generalizing the local convergence analysis of a class of $k$-step iterative algorithms with H

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Basin attractors for various methods
• Enlarging the convergence domain in local convergence studies for iterative methods in Banach spaces
• Increasing the convergence order of an iterative method for nonlinear systems
• Local convergence for an almost sixth order method for solving equations under weak conditions
• On some third-order iterative methods for solving nonlinear equations
• A composite fourth-order iterative method for solving nonlinear equations
• On the local convergence of a fifth-order iterative method in Banach spaces
• New variants of Jarratt's method with sixth-order convergence
• On the local convergence study for an efficient \(k\)-step iterative method
• Local convergence of a Newton-Traub composition in Banach spaces
• Some new variants of Newton's method.
• On the local convergence of fast two-step Newton-like methods for solving nonlinear equations
• Local convergence for multi-point-parametric Chebyshev-Halley-type methods of high convergence order
• Iterative methods of order four and five for systems of nonlinear equations
• Local convergence of a parameter based iteration with Hölder continuous derivative in Banach spaces
• Basins of attraction for optimal eighth order methods to find simple roots of nonlinear equations
• LOCAL CONVERGENCE FOR SOME THIRD-ORDER ITERATIVE METHODS UNDER WEAK CONDITIONS
• Computational Methods in Nonlinear Analysis
• Local convergence of deformed Halley method in Banach space under Holder continuity conditions
• Convergence and Applications of Newton-type Iterations
• Local convergence of modified Halley-like methods
• A variant of Newton's method with accelerated third-order convergence
• A study on the local convergence and the dynamics of Chebyshev-Halley-type methods free from second derivative
• Weerakoon-Fernando method with accelerated third-order convergence for systems of nonlinear equations

This page was built for publication: On the local convergence of Weerakoon-Fernando method with \(\omega\) continuity condition in Banach spaces