Semilocal convergence for Halley's method under weak Lipschitz condition

DOI10.1016/J.AMC.2009.09.055zbMath1187.65059OpenAlexW2082505363MaRDI QIDQ1049319

Xiubin Xu, Yonghui Ling

Publication date: 8 January 2010

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

Full work available at URL: https://doi.org/10.1016/j.amc.2009.09.055

zbMATH Keywords

Banach spacesHalley's methodsemilocal convergenceHammerstein integral equationaffine invariantweak Lipschitz condition

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical methods for integral equations (65R20) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (10)

Semilocal convergence and \(R\)-order for modified Chebyshev-Halley methods ⋮ On the semi-local convergence of Halley's method under a center-Lipschitz condition on the second Fréchet derivative ⋮ Unnamed Item ⋮ Derivative free algorithm for solving nonlinear equations ⋮ New improved convergence analysis for the secant method ⋮ Convergence for a class of improved sixth-order Chebyshev-Halley type methods ⋮ Constructing third-order derivative-free iterative methods ⋮ Higher-order reverse automatic differentiation with emphasis on the third-order ⋮ Convergence behavior for Newton-Steffensen's method under \(\gamma\)-condition of second derivative ⋮ Convergence for modified Halley-like methods with less computation of inversion

Uses Software

• NewtonLib

Cites Work

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• Convergence criterion of Newton's method for singular systems with constant rank derivatives
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• A unified convergence theory for Newton-type methods for zeros of nonlinear operators in Banach spaces
• On the \(R\)-order of the Halley method
• Convergence of the family of the deformed Euler--Halley iterations under the Hölder condition of the second derivative
• Asymptotic Mesh Independence of Newton–Galerkin Methods via a Refined Mysovskii Theorem
• Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
• Classroom Note:Geometry and Convergence of Euler's and Halley's Methods
• Newton's method under weak Kantorovich conditions
• Asymptotic Mesh Independence of Newton's Method Revisited
• Convergence of Newton's method and uniqueness of the solution of equations in Banach space

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