On the comparison of a weak variant of the Newton--Kantorovich and Miranda theorems.

DOI10.1016/J.CAM.2003.10.015zbMath1074.65062OpenAlexW2080269073MaRDI QIDQ1428479

Ioannis K. Argyros

Publication date: 29 March 2004

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.2003.10.015

zbMATH Keywords

Newton-Kantorovich theoremsemi-local convergenceCenter-Lipschitz conditionMiranda partition/domain/conditionsMiranda theoremNewton-Kantrovich hypothesis

Mathematics Subject Classification ID

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

Related Items (7)

Newton-Kantorovich theorem for a family of modified Halley's method under Hölder continuity conditions in Banach space ⋮ On the semilocal convergence of the Halley method using recurrent functions ⋮ Third-order convergence theorem by using majorizing function for a modified Newton method in Banach space ⋮ On the midpoint method for solving equations ⋮ Newton-Kantorovich type convergence theorem for a family of new deformed Chebyshev method ⋮ Convergence theorem for a family of new modified Halley's method in Banach space ⋮ Fourth-order convergence theorem by using majorizing functions for super-Halley method in Banach spaces

Cites Work

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• Some notions of nonstationary multistep iteration processes
• An improved error analysis for Newton-like methods under generalized conditions
• Local convergence of inexact Newton-like iterative methods and applications
• A GENERALIZED THEOREM OF MIRANDA AND THE THEOREM OF NEWTON–KANTOROVICH
• Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
• On The Convergence And Application Of Newton's Method Under Weak HÖlder Continuity Assumptions

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