Error bounds for Newton-like methods under Kantorovich type assumptions

DOI10.1007/BF03167104zbMath0618.65047OpenAlexW2166783837MaRDI QIDQ4728116

Tetsuro Yamamoto

Publication date: 1986

Published in: Japan Journal of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf03167104

zbMATH Keywords

Banach spacesNewton's methoderror boundsa posteriori error estimatesNewton-Kantorovich theoremKantorovich type assumptions

Mathematics Subject Classification ID

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

Related Items (12)

A method for finding sharp error bounds for Newton's method under the Kantorovich assumptions ⋮ On the method of tangent hyperbolas in Banach spaces ⋮ A convergence theorem for Newton-like methods in Banach spaces ⋮ Ball-convergence theorems and error estimates for certain iterative methods for nonlinear equations ⋮ Error bounds for Newton-like methods under Kantorovich type assumptions, II ⋮ A kantorovich-type theorem for inexact newton methods ⋮ Uniqueness of the solution in a Kantorovich-type theorem of Häu\ler for the Gauss-Newton Method ⋮ Extended Newton-type method for nonlinear functions with values in a cone ⋮ A note on a posteriori error bound of zabrejko and nguen for zincenko's iteration ⋮ 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

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