On a theorem of S. Smale about Newton's method for analytic mappings

DOI10.1016/0893-9659(88)90179-6zbMath0631.65064OpenAlexW2069255158MaRDI QIDQ1094827

Werner C. Rheinboldt

Publication date: 1988

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0893-9659(88)90179-6

zbMATH Keywords

convergenceBanach spacesNewton's methodanalytic mappings

Mathematics Subject Classification ID

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

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Convergence of Newton–Kantorovich Approximations to an Approximate Zero ⋮ New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems ⋮ Convergence of starters for solving Kepler's equation via Smale's \(\alpha \)-test ⋮ Newton method under weak Lipschitz continuous derivative in Banach spaces. ⋮ Unified complexity analysis for Newton LP methods ⋮ Newton's method and the Computational Complexity of the Fundamental Theorem of Algebra ⋮ Approximate Zeros of Quadratically Convergent Algorithms ⋮ An extension of a theorem by Wang for Smale's \(\alpha\)-theory and applications ⋮ On the convergence and applications of Newton-like methods for analytic operators ⋮ The theory of Newton's method ⋮ A globally convergent method for finding zeros of smooth functions ⋮ Extended convergence results for the Newton-Kantorovich iteration

Cites Work

• A method for finding sharp error bounds for Newton's method under the Kantorovich assumptions
• Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
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