On the convergence of inexact two-point Newton-like methods on Banach spaces
From MaRDI portal
Publication:1664278
DOI10.1016/j.amc.2015.05.127zbMath1410.65213OpenAlexW842559037MaRDI QIDQ1664278
Ioannis K. Argyros, Ángel Alberto Magreñán
Publication date: 24 August 2018
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.amc.2015.05.127
semilocal convergenceBanach spacelocal convergencedivided difference of order oneinexact Newton-like methodsunivariate unconstrained optimization
Nonlinear programming (90C30) Iterative procedures involving nonlinear operators (47J25) Numerical solutions to equations with nonlinear operators (65J15)
Related Items
The convergence ball and error analysis of the two-step secant method ⋮ A new convergence analysis and perturbation resilience of some accelerated proximal forward–backward algorithms with errors ⋮ Semilocal Convergence Theorem for a Newton-like Method ⋮ The convergence ball and error analysis of the relaxed secant method ⋮ Weaker conditions for inexact mutitpoint Newton-like methods
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Different anomalies in a Jarratt family of iterative root-finding methods
- Expanding the applicability of inexact Newton methods under Smale's (\(\alpha\), \(\gamma\))-theory
- A new tool to study real dynamics: the convergence plane
- Expanding the applicability of Newton's method using Smale's \(\alpha\)-theory
- Weaker conditions for the convergence of Newton's method
- Dynamics of a new family of iterative processes for quadratic polynomials
- On the semilocal convergence of Newton-Kantorovich method under center-Lipschitz conditions
- Recurrence relations for the super-Halley method
- Third-order iterative methods for operators with bounded second derivative
- Geometric constructions of iterative functions to solve nonlinear equations
- Some variant of Newton's method with third-order convergence.
- A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space
- On the local convergence of fast two-step Newton-like methods for solving nonlinear equations
- Third-order methods on Riemannian manifolds under Kantorovich conditions
- Reducing chaos and bifurcations in Newton-type methods
- Computational theory of iterative methods.
- Newton-type methods on Riemannian manifolds under Kantorovich-type conditions
- On a characterization of some Newton-like methods of \(R\)-order at least three
- Convergence ball of a modified secant method for finding zero of derivatives
- A new unidimensional search method for optimization: linear interpolation method
- On modified Newton methods with cubic convergence
- On a two-step relaxed Newton-type method
- On Newton-like methods
- A semilocal convergence analysis for directional Newton methods
- The majorant method in the theory of newton-kantorovich approximations and the pták error estimates
- Convergence domains of certain iterative methods for solving nonlinear equations
- Inexact Newton Methods
- The inexact, inexact perturbed, and quasi-Newton methods are equivalent models
- Resolution of quadratic equations in banach spaces
- Modification of the Kantorovich assumptions for semilocal convergence of the Chebyshev method
- A variant of Newton's method with accelerated third-order convergence
- Chebyshev's approximation algorithms and applications
