A cubically convergent Newton-type method under weak conditions

DOI10.1016/j.cam.2007.08.013zbMath1146.65042OpenAlexW1998718959MaRDI QIDQ939542

Zhongyong Hu, Liang Fang, Guo-Ping He

Publication date: 22 August 2008

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2007.08.013

zbMATH Keywords

Newton's methoditerative methodnonlinear equationsthird-order convergence

Mathematics Subject Classification ID

Numerical computation of solutions to single equations (65H05)

Related Items (6)

A novel cubically convergent iterative method for computing complex roots of nonlinear equations ⋮ A fourth-order derivative-free algorithm for nonlinear equations ⋮ Modifications of higher-order convergence for solving nonlinear equations ⋮ On a Newton-type method under weak conditions with dynamics ⋮ Note on a cubically convergent Newton-type method under weak conditions ⋮ Some modifications of Newton's method with higher-order convergence for solving nonlinear equations

Cites Work

• Construction of Newton-like iteration methods for solving nonlinear equations
• A modified Newton method for rootfinding with cubic convergence.
• Some variant of Newton's method with third-order convergence.
• Third-order methods from quadrature formulae for solving systems of nonlinear equations.
• A new continuation Newton-like method and its deformation
• The theory of Newton's method
• On Newton-type methods with cubic convergence
• Some new variants of Newton's method.
• A modified Newton method with cubic convergence: the multivariate case
• A variant of Newton's method with accelerated third-order convergence

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