The Kantorovich Theorem with Optimal Error Bounds
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Publication:4194369
DOI10.2307/2321528zbMath0407.65023OpenAlexW4248935348MaRDI QIDQ4194369
Publication date: 1979
Published in: The American Mathematical Monthly (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2307/2321528
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 (21)
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 ⋮ Majorizing Sequences and Error Bounds for Iterative Methods ⋮ A convergence theorem for Newton-like methods in Banach spaces ⋮ Kantorovich-ostrowski convergence theorems and optimal error bounds for jarratt's iterative method ⋮ Error bounds for Newton-like methods under Kantorovich type assumptions, II ⋮ An updated version of the Kantorovich theorem for Newton's method ⋮ Recurrence relations for rational cubic methods. I: The Halley method ⋮ Accessibility Of Solutions By Newton's Method ⋮ New improved convergence analysis for Newton-like methods with applications ⋮ The Kantorovich theorem and interior point methods ⋮ Unified error analysis for Newton-type 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 ⋮ A short survey on Kantorovich
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