Achieving an extended convergence analysis for the secant method under a restricted Hölder continuity condition

DOI10.1007/s40324-020-00234-xzbMath1476.65092OpenAlexW3121003276MaRDI QIDQ2062261

Ioannis K. Argyros, Hongmin Ren

Publication date: 27 December 2021

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

Full work available at URL: https://doi.org/10.1007/s40324-020-00234-x

zbMATH Keywords

error estimatesHölder continuityBanach spacelocal convergencesecant method

Mathematics Subject Classification ID

Newton-type methods (49M15) Numerical solutions to equations with nonlinear operators (65J15)

Cites Work

• Solving non-differentiable equations by a new one-point iterative method with memory
• On an improved local convergence analysis for the Secant method
• A new semilocal convergence theorem for the secant method under Hölder continuous divided differences
• Local convergence of inexact methods under the Hölder condition
• Regula-falsi-Verfahren mit konsistenter Steigung und Majorantenprinzip
• Exact order of convergence of the secant method
• An improved error analysis for Newton-like methods under generalized conditions
• The convergence ball of Newton's method and the uniqueness ball of equations under Hölder-type continuous derivatives
• The secant method and divided differences Hölder continuous
• A uniparametric family of iterative processes for solving nondifferentiable equations
• The secant method for nondifferentiable operators
• Semilocal convergence of the secant method under mild convergence conditions of differentiability
• Newton-Kantorovich approximations under weak continuity conditions
• Computational theory of iterative methods.
• The convergence ball of the secant method under Hölder continuous divided differences
• On a two-step relaxed Newton-type method
• ON THE CONVERGENCE OF A NEWTON-LIKE METHOD UNDER WEAK CONDITIONS
• New sufficient convergence conditions for the secant method
• Convergence and Complexity of Newton Iteration for Operator Equations
• Kantorovich-Like Convergence Theorems for Newton’s Method Using Restricted Convergence Domains
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