Extended local and semilocal convergence for interpolatory iterative methods for nonlinear equations

DOI10.1007/S40324-021-00259-WOpenAlexW3184681563MaRDI QIDQ2101692

Ioannis K. Argyros, Halyna Yarmola, S. M. Shakhno

Publication date: 6 December 2022

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

Full work available at URL: https://doi.org/10.1007/s40324-021-00259-w

zbMATH Keywords

nonlinear equationdivided differenceconvergence orderKurchatov methodlocal and semilocal convergenceLipschitz and Hölder conditionspotra method

Mathematics Subject Classification ID

Newton-type methods (49M15) Numerical computation of solutions to systems of equations (65H10) Iterative procedures involving nonlinear operators (47J25) Numerical solutions to equations with nonlinear operators (65J15) Error analysis and interval analysis (65G99) Numerical analysis (65-XX)

Cites Work

• On an efficient \(k\)-step iterative method for nonlinear equations
• On two families of high order Newton type methods
• On the difference method with quadratic convergence for solving nonlinear operator equations
• A Kantorovich-type analysis for a fast iterative method for solving nonlinear equations
• Iterative Methods and Their Dynamics with Applications
• On an iterative algorithm of order 1.839… for solving nonlinear operator equations^∗)
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