Improved convergence analysis for Newton-like methods

DOI10.1007/S11075-015-0025-3zbMath1339.65074OpenAlexW1195361783MaRDI QIDQ281471

Ioannis K. Argyros, Ángel Alberto Magreñán

Publication date: 11 May 2016

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-015-0025-3

zbMATH Keywords

Banach spacesnumerical examplessemilocal convergenceNewton methodnonlinear operator equations

Mathematics Subject Classification ID

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

Related Items (7)

Extending the applicability of high-order iterative schemes under Kantorovich hypotheses and restricted convergence regions ⋮ On a two-step optimal Steffensen-type method: relaxed local and semi-local convergence analysis and dynamical stability ⋮ Extensions of Kantorovich-type theorems for Newton’s method ⋮ Unnamed Item ⋮ On the complexity of extending the convergence region for Traub's method ⋮ Expanding the applicability of Newton’s method and of a robust modified Newton’s method ⋮ Highly efficient solvers for nonlinear equations in Banach space

Cites Work

• Weaker conditions for the convergence of Newton's method
• A convergence theorem for Newton-like methods in Banach spaces
• An updated version of the Kantorovich theorem for Newton's method
• Untere Fehlerschranken für Regula-Falsi-Verfahren
• Secant-like methods for solving nonlinear integral equations of the Hammerstein type
• Computational theory of iterative methods.
• A multipoint method of third order
• Infinite dimensional multipoint methods and the solution of two point boundary value problems
• New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems
• The Kantorovich Theorem with Optimal Error Bounds
• Adaptive Approximation of Nonlinear Operators
• Optimal Error Bounds for the Newton–Kantorovich Theorem
• The inexact, inexact perturbed, and quasi-Newton methods are equivalent models
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