Note on a cubically convergent Newton-type method under weak conditions

DOI10.1007/S10440-009-9470-0zbMath1198.41010OpenAlexW2005643389MaRDI QIDQ970476

Hao Liu, Hai-Jun Wang

Publication date: 19 May 2010

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10440-009-9470-0

zbMATH Keywords

Newton's methoditerative methodnonlinear equationorder of convergenceapproximated function

Mathematics Subject Classification ID

Rate of convergence, degree of approximation (41A25)

Related Items (4)

Variant of Newton's method using Simpson's 3/8th rule ⋮ On a Newton-type method under weak conditions with dynamics ⋮ Two optimal general classes of iterative methods with eighth-order ⋮ A derivative free globally convergent method and its deformations

Cites Work

• Unnamed Item
• An improvement of the Euler-Chebyshev iterative method
• A class of exponential quadratically convergent iterative formulae for unconstrained optimization
• A generalization of Müller's iteration method based on standard information
• A cubically convergent Newton-type method under weak conditions
• Several new third-order iterative methods for solving nonlinear equations
• Modified families of Newton, Halley and Chebyshev methods
• Selection of good algorithms from a family of algorithms for polynomial derivative evaluation
• Geometric constructions of iterative functions to solve nonlinear equations
• Some variant of Newton's method with third-order convergence.
• Study on gas kinetic unified algorithm for flows from rarefied transition to continuum.
• A new continuation Newton-like method and its deformation
• On Newton-type methods with cubic convergence
• Construction of third-order modifications of Newton's method
• On some families of multi-point iterative methods for solving nonlinear equations
• On modified Newton methods with cubic convergence
• On K nig's root-finding algorithms*
• A Family of Fourth Order Methods for Nonlinear Equations
• An acceleration of Newton's method: Super-Halley method
• A variant of Newton's method with accelerated third-order convergence

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