MODIFICATION OF THE KANTOROVICH-TYPE CONDITIONS FOR NEWTON'S METHOD INVOLVING TWICE FRECHET DIFFERENTIABLE OPERATORS

DOI10.1142/S1793557113500265zbMath1408.65034MaRDI QIDQ2868575

Santhosh George, Ioannis K. Argyros

Publication date: 17 December 2013

Published in: Asian-European Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Newton's methodsemilocal convergenceBanach spaceFréchet derivativemajorizing sequence

Mathematics Subject Classification ID

Numerical solutions to equations with nonlinear operators (65J15) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)

Cites Work

• Unnamed Item
• Weaker conditions for the convergence of Newton's method
• A new semilocal convergence theorem for Newton's method
• A note on the Kantorovich theorem for Newton iteration
• Relaxing convergence conditions for Newton's method
• A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space
• Convergence and Applications of Newton-type Iterations
• A Newton-Kantorovich theorem for equations involving \(m\)-Fréchet differentiable operators and applications in radiative transfer

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