A unified derivation of several error bounds for Newton's process

DOI10.1016/0377-0427(85)90015-9zbMath0582.65047OpenAlexW2057500966MaRDI QIDQ1068524

Tetsuro Yamamoto

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1016/0377-0427(85)90015-9

zbMATH Keywords

Newton's methoderror boundsBanach spaceKantorovich theorempartially ordered space

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical solutions to equations with nonlinear operators (65J15) Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces (47H07)

Related Items

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, A unifying theorem on newton's method, Error bounds for Newton-like methods under Kantorovich type assumptions, II, Mixed precision path tracking for polynomial homotopy continuation, The Kantorovich theorem and interior point methods, Some notes on split Newton iterative algorithm, 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, On mesh independence and Newton-type methods, A short survey on Kantorovich

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