On the Convergence of Secant-Like Methods

DOI10.1007/978-3-030-15242-0_5zbMath1435.65083OpenAlexW2969701817MaRDI QIDQ5110830

M. J. Rubio, Miguel Ángel Hernández-Verón, Ioannis K. Argyros

Publication date: 25 May 2020

Published in: Current Trends in Mathematical Analysis and Its Interdisciplinary Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-15242-0_5

zbMATH Keywords

iterative methodsemilocal convergencenonlinear equationlocal convergencesecant methoddivided differencenon-differentiable operator

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical solutions to equations with nonlinear operators (65J15)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Local convergence of efficient secant-type methods for solving nonlinear equations
• On the approximation of derivatives using divided difference operators preserving the local convergence order of iterative methods
• On the ball of convergence of secant-like methods for non-differentiable operators
• An analysis of the semilocal convergence for secant-like methods
• On an improved local convergence analysis for the Secant method
• The Newton-Kantorovich method under mild differentiability conditions and the Ptâk error estimates
• Newton-like methods for the computation of fixed points
• New approach for numerical solution of Hammerstein integral equations
• Homocentric convergence ball of the secant method
• The secant method and fixed points of nonlinear operators
• Regula-falsi-Verfahren mit konsistenter Steigung und Majorantenprinzip
• Chebyshev method and convexity
• Some methods for finding error bounds for Newton-like methods under mild differentiability conditions
• A convergence theorem for Newton-like methods under generalized Chen- Yamamoto-type assumptions
• New recurrence relations for Chebyshev method
• On a higher order secant method.
• A modified secant method for semismooth equations
• A uniparametric family of iterative processes for solving nondifferentiable equations
• Secant-like methods for solving nonlinear integral equations of the Hammerstein type
• On the secant method
• Convergence analysis of the secant type methods
• A Steffensen's type method in Banach spaces with applications on boundary-value problems
• The convergence ball of the secant method under Hölder continuous divided differences
• Newton's method under mild differentiability conditions with error analysis
• Solving a special case of conservative problems by secant-like methods
• A UNIFIED CONVERGENCE ANALYSIS FOR SECANT-TYPE METHODS
• A note on a posteriori error bound of zabrejko and nguen for zincenko's iteration
• Newton-like methods under mild differentiability conditions with error analysis
• Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
• Multipoint Super-Halley Type Approximation Algorithms in Banach Spaces
• A New Collocation-Type Method for Hammerstein Integral Equations
• A new type of recurrence relations for the secant method^∗
• Numerical Solvability of Hammerstein Integral Equations of Mixed Type

This page was built for publication: On the Convergence of Secant-Like Methods