On a convex acceleration of Newton's method

DOI10.1023/A:1021730118905zbMath0915.90235OpenAlexW61253812MaRDI QIDQ1280098

José Antonio Ezquerro, Miguel A. Hernández

Publication date: 17 May 1999

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

Full work available at URL: https://doi.org/10.1023/a:1021730118905

zbMATH Keywords

nonlinear equationsmajorizing sequencesconvex acceleration of Newton's methodNewton-Kantorovich assumptions

Mathematics Subject Classification ID

Nonlinear programming (90C30) Numerical computation of solutions to systems of equations (65H10)

Related Items (11)

Higher-order method for the solution of a nonlinear scalar equation ⋮ An analysis of the properties of the variants of Newton's method with third order convergence ⋮ Halley's method for operators with unbounded second derivative ⋮ Semilocal convergence of a continuation method with Hölder continuous second derivative in Banach spaces ⋮ Dynamical aspects of some convex acceleration methods as purely iterative algorithm for Newton's maps ⋮ Super-Halley method under majorant conditions in Banach spaces ⋮ Unnamed Item ⋮ Convergence of a parameter based iterative method for solving nonlinear equations in Banach spaces ⋮ Graphic and numerical comparison between iterative methods ⋮ Convergence analysis of a variant of the Newton method for solving nonlinear equations ⋮ Deformed super-Halley's iteration in Banach spaces and its local and semilocal convergence

Cites Work

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• A note on Halley's method
• On the method of tangent hyperbolas in Banach spaces
• Some methods for finding error bounds for Newton-like methods under mild differentiability conditions
• A local convergence theorem for the super-Halley method in a Banach space
• Convergence results for the Super-Halley method using divided differences
• On an iterative algorithm of order 1.839… for solving nonlinear operator equations^∗)
• Accessibility Of Solutions By Newton's Method
• A Unified Convergence Theory for a Class of Iterative Processes

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