Unified error analysis for Newton-type methods

DOI10.1007/BF01399322zbMath0402.65038MaRDI QIDQ1255768

George J. Miel

Publication date: 1979

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/132650

zbMATH Keywords

Error AnalysisNewton-Type MethodsNonlinear Operativ EquationsRounding Errors

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Iterative procedures involving nonlinear operators (47J25) Numerical solutions to equations with nonlinear operators (65J15)

Related Items

Majorizing Sequences and Error Bounds for Iterative Methods, A convergence theorem for Newton-like methods in Banach spaces, Sharp error bounds for Newton-like methods under weak smoothness assumptions, On the convergence of Newton-like methods using restricted domains, A unified approach for the convergence of certain numerical algorithms, using recurrent functions, Majorizing sequences for iterative methods, Weak convergence conditions for inexact Newton-type methods, An error analysis for the secant method, Kantorovich-Like Convergence Theorems for Newton’s Method Using Restricted Convergence Domains, Extended Newton-type method for nonlinear functions with values in a cone, New conditions for the convergence of Newton-like methods and applications, On the convergence of Newton-type methods under mild differentiability conditions, The theory of Newton's method

Cites Work

• Unnamed Item
• Error analysis for the Newton-Raphson method
• Newton's method under mild differentiability conditions with error analysis
• The Kantorovich Theorem with Optimal Error Bounds
• Optimal Error Bounds for the Newton–Kantorovich Theorem