Some modifications of Newton's method with fifth-order convergence

DOI10.1016/j.cam.2006.10.072zbMath1130.41005OpenAlexW2086223268MaRDI QIDQ2475337

Yitian Li, Xiuhua Wang, Jisheng Kou

Publication date: 11 March 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.2006.10.072

zbMATH Keywords

Newton's methoditerative methodnonlinear equationsroot-finding

Mathematics Subject Classification ID

Rate of convergence, degree of approximation (41A25) Numerical approximation and computational geometry (primarily algorithms) (65D99)

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Cites Work

• Unnamed Item
• Unnamed Item
• An improvement of the Euler-Chebyshev iterative method
• Modified Newton's method with third-order convergence and multiple roots
• 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.
• 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