Concerning the convergence of Newton's method and quadratic majorants

DOI10.1007/s12190-008-0140-6zbMath1180.65064OpenAlexW2064385111MaRDI QIDQ1032560

Ioannis K. Argyros

Publication date: 26 October 2009

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

Full work available at URL: https://doi.org/10.1007/s12190-008-0140-6

zbMATH Keywords

Newton's methodBanach spaceFréchet-derivativeKantorovich's theoremweaker assumptionslarger convergence regionquadratic majorantsemilinear convergence

Mathematics Subject Classification ID

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

Related Items

Extending the applicability of the Gauss-Newton method for convex composite optimization using restricted convergence domains and average Lipschitz conditions ⋮ Improved local convergence of Newton's method under weak majorant condition ⋮ Expanding the applicability of the Gauss-Newton method for convex optimization under a majorant condition ⋮ Elliptic quadratic operator equations ⋮ Local convergence analysis of inexact Gauss-Newton method for singular systems of equations under majorant and center-majorant condition ⋮ Expanding the applicability of the Kantorovich's theorem for solving generalized equations using Newton's method ⋮ General convergence conditions of Newton's method for \(m\)-Fréchet differentiable operators

Cites Work

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• Accessibility Of Solutions By Newton's Method