On Newton's method under Hölder continuous derivative

DOI10.1016/S0022-247X(02)00060-4zbMath1006.65053OpenAlexW2043877248MaRDI QIDQ1614692

Zhengda Huang

Publication date: 8 September 2002

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0022-247x(02)00060-4

zbMATH Keywords

convergencenumerical exampleNewton's methodBanach spacenonlinear operator equationtwo point boundary value problemHölder continuous derivative

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Nonlinear boundary value problems for ordinary differential equations (34B15) Numerical solutions to equations with nonlinear operators (65J15) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

Related Items (7)

A generalization of the Banach contraction principle with high order of convergence of successive approximations ⋮ Local convergence of inexact methods under the Hölder condition ⋮ A convergence theorem for the inexact Newton methods based on Hölder continuous Fréchet derivative ⋮ Fixed point theorems for \(\varphi\)-contractions ⋮ Generalized quasilinearization versus Newton method ⋮ Mysovskii-type theorem for the Secant method under Hölder continuous Fréchet derivative ⋮ On the local convergence of inexact Newton-type methods under residual control-type conditions

Cites Work

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• On Newton's method under mild differentiability conditions and applications
• Local and global behavior for algorithms of solving equations
• Relaxing convergence conditions for Newton's method
• Newton's method under mild differentiability conditions with error analysis
• Convergence of Newton’s method and inverse function theorem in Banach space

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