A Newton-Kantorovich theorem for equations involving \(m\)-Fréchet differentiable operators and applications in radiative transfer

DOI10.1016/S0377-0427(00)00317-4zbMath0983.65069MaRDI QIDQ5939866

Ioannis K. Argyros

Publication date: 7 April 2002

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

zbMATH Keywords

convergencenumerical exampleNewton's methoderror boundsBanach spaceradiative transfernonlinear operator equationnonlinear integral equationFréchet-differentiable operatormultilinear operators

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Other nonlinear integral equations (45G10) Numerical solutions to equations with nonlinear operators (65J15) Radiative transfer in astronomy and astrophysics (85A25)

Related Items (12)

On the Newton-Kantorovich hypothesis for solving equations ⋮ A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space ⋮ On a result by Dennis and Schnabel for Newton's method: further improvements ⋮ Extending the applicability of Newton's method for \(k\)-Fréchet differentiable operators in Banach spaces ⋮ Extending the applicability of Newton's method by improving a local result due to Dennis and Schnabel ⋮ Expanding the applicability of a third order Newton-type method free of bilinear operators ⋮ An extension of Gander's result for quadratic equations ⋮ A new semilocal convergence theorem for Newton's method involving twice Fréchet-differen\-tiabil\-ity at only one point ⋮ Two conditions concerning Newton's method ⋮ General convergence conditions of Newton's method for \(m\)-Fréchet differentiable operators ⋮ On the convergence and applications of Newton-like methods for analytic operators ⋮ MODIFICATION OF THE KANTOROVICH-TYPE CONDITIONS FOR NEWTON'S METHOD INVOLVING TWICE FRECHET DIFFERENTIABLE OPERATORS

Cites Work

• A new semilocal convergence theorem for Newton's method
• A note on the Kantorovich theorem for Newton iteration
• A new convergence theorem for the Jarratt method in Banach space
• A convergence theorem for Newton-like methods under generalized Chen- Yamamoto-type assumptions
• Some notions of nonstationary multistep iteration processes
• On the approximation of some nonlinear equations
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