An improved unifying convergence analysis of Newton's method in Riemannian manifolds

DOI10.1007/BF02832359zbMath1136.65055WikidataQ115391520 ScholiaQ115391520MaRDI QIDQ2471342

Ioannis K. Argyros

Publication date: 22 February 2008

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

zbMATH Keywords

Newton's methodRiemannian manifolderror boundsNewton-Kantorovich methodlocal/semilocal convergencesingularity of a vector field

Mathematics Subject Classification ID

Singularities of vector fields, topological aspects (58K45) Numerical solutions to equations with nonlinear operators (65J15)

Related Items

Newton-type methods on Riemannian manifolds under Kantorovich-type conditions ⋮ Kantorovich's theorem on Newton's method under majorant condition in Riemannian manifolds ⋮ Chebyshev-Halley's method on Riemannian manifolds ⋮ On a bilinear operator free third order method on Riemannian manifolds ⋮ Traub-type high order iterative procedures on Riemannian manifolds ⋮ Third-order methods on Riemannian manifolds under Kantorovich conditions ⋮ ON THE SEMILOCAL CONVERGENCE OF NEWTON'S METHOD FOR SECTIONS ON RIEMANNIAN MANIFOLDS ⋮ Extending the applicability of Newton's method on Lie groups ⋮ A framework for generalising the Newton method and other iterative methods from Euclidean space to manifolds ⋮ Newton's method for approximating zeros of vector fields on Riemannian manifolds ⋮ EXTENDING THE APPLICABILITY OF NEWTON'S METHOD ON RIEMANNIAN MANIFOLDS WITH VALUES IN A CONE

Cites Work

• A unifying local convergence result for Newton's method in Riemannian manifolds
• Kantorovich's theorem on Newton's method in Riemannian manifolds
• A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space
• The majorant method in the theory of newton-kantorovich approximations and the pták error estimates
• An Improved Convergence Analysis and Applications for Newton-Like Methods in Banach Space
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