Majorizing Sequences and Error Bounds for Iterative Methods

DOI10.2307/2006227zbMath0425.65033OpenAlexW4248585806MaRDI QIDQ3860749

George J. Miel

Publication date: 1980

Full work available at URL: https://doi.org/10.2307/2006227

zbMATH Keywords

error boundsiterative methodsBanach spacemajorizing sequencessemi-local convergence theorems

Mathematics Subject Classification ID

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

Related Items (28)

A Kantorovich-type convergence analysis for the Gauss-Newton-method ⋮ On the Newton-Kantorovich hypothesis for solving equations ⋮ A method for finding sharp error bounds for Newton's method under the Kantorovich assumptions ⋮ Weak sufficient convergence conditions and applications for Newton methods ⋮ A convergence theorem for Newton-like methods in Banach spaces ⋮ New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems ⋮ On the convergence of Newton-like methods using restricted domains ⋮ A unified approach for the convergence of certain numerical algorithms, using recurrent functions ⋮ On a two-step optimal Steffensen-type method: relaxed local and semi-local convergence analysis and dynamical stability ⋮ Error bounds for Newton-like methods under Kantorovich type assumptions, II ⋮ Majorizing sequences for iterative methods ⋮ An improved error analysis for Newton-like methods under generalized conditions ⋮ An updated version of the Kantorovich theorem for Newton's method ⋮ Error bounds of Newton type process on Banach spaces ⋮ Kantorovich-Like Convergence Theorems for Newton’s Method Using Restricted Convergence Domains ⋮ A convergence theorem for the Newton-like methods under some kind of weak Lipschitz conditions ⋮ Extended Newton-type method for nonlinear functions with values in a cone ⋮ Convergence behaviour of inexact Newton methods under weak Lipschitz condition. ⋮ New conditions for the convergence of Newton-like methods and applications ⋮ A convergence theorem for Newton’s method in Banach spaces ⋮ Error bounds for Newton-like methods under Kantorovich type assumptions ⋮ On the convergence of Newton-type methods under mild differentiability conditions ⋮ A note on Newton type iterative methods ⋮ Historical developments in convergence analysis for Newton's and Newton-like methods ⋮ The theory of Newton's method ⋮ Error bounds for Newton's iterates derived from the Kantorovich theorem ⋮ Some methods for finding error bounds for Newton-like methods under mild differentiability conditions ⋮ A unified derivation of several error bounds for Newton's process

Cites Work

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• Quadratic equations in Banach spaces
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• On a Posteriori Error Estimates
• Quasi-Newton Methods, Motivation and Theory
• Exit Criteria for Newton–Cotes Quadrature Rules
• On Newton-Iterative Methods for the Solution of Systems of Nonlinear Equations
• The Kantorovich Theorem with Optimal Error Bounds
• A Characterization of Superlinear Convergence and Its Application to Quasi-Newton Methods
• Optimal Error Bounds for the Newton–Kantorovich Theorem
• A Unified Convergence Theory for a Class of Iterative Processes
• The Newton-Kantorovich Theorem
• A Note on the Convergence of Newton’s Method

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