On a theorem of L.V. Kantorovich concerning Newton's method.

DOI10.1016/S0377-0427(02)00865-8zbMath1040.65044MaRDI QIDQ1811585

Ioannis K. Argyros

Publication date: 17 June 2003

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

zbMATH Keywords

Newton's methodBanach spaceFréchet derivativeconvergence theoremKantorovich'sLocal-semilocal convergenceRadius of convergence

Mathematics Subject Classification ID

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

Related Items (11)

On the convergence of Newton's method for a class of nonsmooth operators ⋮ On the domain of starting points of Newton's method under center Lipschitz conditions ⋮ A Newton-type method and its application ⋮ Kurchatov-type methods for non-differentiable Hammerstein-type integral equations ⋮ Center conditions on high order derivatives in the semilocal convergence of Newton's method ⋮ A variant of Newton's method and its application ⋮ A new semilocal convergence theorem for Newton's method involving twice Fréchet-differen\-tiabil\-ity at only one point ⋮ Third-order convergence theorem by using majorizing function for a modified Newton method in Banach space ⋮ On a nonsmooth version of Newton's method using locally Lipschitzian operators ⋮ Enlarging the domain of starting points for Newton's method under center conditions on the first Fréchet-derivative ⋮ On global convergence for an efficient third-order iterative process

Cites Work

• A new semilocal convergence theorem for Newton's method
• A note on the Kantorovich theorem for Newton iteration
• Some notions of nonstationary multistep iteration processes
• The theory of Newton's method
• A new semilocal convergence theorem for Newton's method in Banach space using hypotheses on the second Fréchet-derivative
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