ON THE SEMILOCAL CONVERGENCE OF NEWTON'S METHOD FOR SECTIONS ON RIEMANNIAN MANIFOLDS

DOI10.1142/S1793557114500077zbMath1296.65082WikidataQ115244549 ScholiaQ115244549MaRDI QIDQ5417509

Santhosh George, Ioannis K. Argyros

Publication date: 21 May 2014

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

zbMATH Keywords

Newton's methodRiemannian manifoldsemilocal convergencenonlinear operator equation

Mathematics Subject Classification ID

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

Cites Work

• Unnamed Item
• Unnamed Item
• Weaker conditions for the convergence of Newton's method
• Newton's method for sections on Riemannian manifolds: Generalized covariant \(\alpha \)-theory
• A unifying local convergence result for Newton's method in Riemannian manifolds
• Newton's method for approximating zeros of vector fields on Riemannian manifolds
• Newton's method on Lie groups
• Minimizing a differentiable function over a differential manifold
• Kantorovich's theorem on Newton's method in Riemannian manifolds
• An improved unifying convergence analysis of Newton's method in Riemannian manifolds
• Computational Methods in Nonlinear Analysis
• A semilocal convergence analysis for directional Newton methods
• Newton's method on Riemannian manifolds and a geometric model for the human spine
• Convergence and Applications of Newton-type Iterations
• The majorant method in the theory of newton-kantorovich approximations and the pták error estimates
• Newton's method on Riemannian manifolds: covariant alpha theory