The convergence theorem for fourth-order super-Halley method in weaker conditions

DOI10.1186/s13660-016-1227-5zbMath1349.65188OpenAlexW2550387898WikidataQ59468559 ScholiaQ59468559MaRDI QIDQ343542

Lin Zheng

Publication date: 28 November 2016

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-016-1227-5

zbMATH Keywords

nonlinear equations in Banach spacessemilocal convergencesuper-Halley methodNewton-Kantorovich theoremweaker conditions

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)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Semilocal convergence of a class of modified super-Halley methods in Banach spaces
• Third-order iterative methods with applications to Hammerstein equations: a unified approach
• Recurrence relations for rational cubic methods. II: The Chebyshev method
• A variant of super-Halley method with accelerated fourth-order convergence
• Recurrence relations for rational cubic methods. I: The Halley method
• Recurrence relations for semilocal convergence of a Newton-like method in Banach spaces
• General study of iterative processes of \(R\) -order at least three under weak convergence conditions
• On a class of Newton-like methods for solving nonlinear equations
• Recurrence relations for the super-Halley method
• The application of an inverse-free Jarratt-type approximation to nonlinear integral equations of Hammerstein-type
• On the convergence of trust region algorithms for unconstrained minimization without derivatives
• On the semilocal convergence of the Halley method using recurrent functions
• Recurrence relations for a Newton-like method in Banach spaces
• New iterations of \(R\)-order four with reduced computational cost
• Semilocal convergence of a multipoint fourth-order super-Halley method in Banach spaces
• An adaptive version of a fourth-order iterative method for quadratic equations
• A Newton-Kantorovich convergence theorem for the inverse-free Jarratt method in Banach space
• Fourth-order convergence theorem by using majorizing functions for super-Halley method in Banach spaces
• On a third-order Newton-type method free of bilinear operators

This page was built for publication: The convergence theorem for fourth-order super-Halley method in weaker conditions