Convergence of general iteration schemes

DOI10.1016/0022-247X(92)90188-JzbMath0767.65050OpenAlexW2085222329MaRDI QIDQ1206827

Ioannis K. Argyros, Ferenc Szidarovszky

Publication date: 1 April 1993

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-247x(92)90188-j

zbMATH Keywords

convergencenonlinear difference equationstime dependenthigher orderiteration schemespoint-to-set mapsdiscrete time scale Lyapunov theory

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (6)

A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space ⋮ Comparison theorems for algorithmic models ⋮ Iterative processes: A survey of convergence theory using Lyapunov second method ⋮ Sufficient convergence conditions for iteration schemes modelled by point-to-set mappings ⋮ A new iterative method of asymptotic order 1+√2 for the computation of fixed points ⋮ On a two-point Newton-like method of convergent order two

Cites Work

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• Principles and procedures of numerical analysis
• Global asymptotic stability of non-linear difference equations
• Global asymptotic stability of non-linear difference equations. II
• The secant method and fixed points of nonlinear operators
• Expectations and stability in oligopoly models
• Global asymptotic stability in discrete systems
• A comparative study of several general convergence conditions for algorithms modeled by point-to-set maps
• The Stability of Dynamic Processes
• On the Convergence of Algorithms with Implications for Stochastic and Nondifferentiable Optimization

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