An updated version of the Kantorovich theorem for Newton's method

DOI10.1007/BF02237981zbMath0458.65046OpenAlexW1724093578MaRDI QIDQ1151725

George J. Miel

Publication date: 1981

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02237981

zbMATH Keywords

Newton methodKantorovich theoremGragg-Tapia error boundsq-quadratic convergence

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

Optimizing the applicability of a theorem by F. Potra for Newton-like methods ⋮ Improved convergence analysis for Newton-like methods ⋮ A method for finding sharp error bounds for Newton's method under the Kantorovich assumptions ⋮ 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 ⋮ Error bounds for Newton-like methods under Kantorovich type assumptions, II ⋮ Recurrence relations for rational cubic methods. I: The Halley method ⋮ New improved convergence analysis for Newton-like methods with applications ⋮ The Kantorovich theorem and interior point methods ⋮ Recurrence relations for rational cubic methods. II: The Chebyshev method ⋮ A convergence theorem for Newton’s method in Banach spaces ⋮ Error bounds for Newton-like methods under Kantorovich type assumptions ⋮ 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 ⋮ A unified derivation of several error bounds for Newton's process

Cites Work

• Semilocal analysis of equations with smooth operators
• Sharp error bounds for Newton's process
• The rate of convergence of Newton's process
• The method of successive approximations for functional equations
• A Globally Convergent Ball Newton Method
• Majorizing Sequences and Error Bounds for Iterative Methods
• A Comparison of the Existence Theorems of Kantorovich and Moore
• Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
• The Kantorovich Theorem with Optimal Error Bounds
• Optimal Error Bounds for the Newton–Kantorovich Theorem
• The Newton-Kantorovich Theorem
• The Kantorovich Theorem for Newton's Method
• On the Kantorovich Hypothesis for Newton’s Method
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