Smale's point estimate theory for Newton's method on Lie groups

DOI10.1016/j.jco.2008.11.001zbMath1170.65040OpenAlexW2013010587WikidataQ115350163 ScholiaQ115350163MaRDI QIDQ1023398

Chong Li, Jean-Pierre Dedieu, Jin-Hua Wang

Publication date: 11 June 2009

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jco.2008.11.001

zbMATH Keywords

convergenceNewton's methodRiemannian manifoldinitial value problems\(\gamma\)-conditionLie GroupSmale's point estimate theory

Mathematics Subject Classification ID

Nonlinear differential equations in abstract spaces (34G20) Numerical solutions to equations with nonlinear operators (65J15) Implicit function theorems; global Newton methods on manifolds (58C15)

Related Items (20)

Local convergence analysis of inexact Newton method with relative residual error tolerance under majorant condition in Riemannian manifolds ⋮ Newton-type methods on Riemannian manifolds under Kantorovich-type conditions ⋮ Finding geodesics joining given points ⋮ New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems ⋮ Local convergence analysis of Newton's method for solving strongly regular generalized equations ⋮ Local convergence of the Newton’s method in two step nilpotent Lie groups ⋮ Kantorovich's theorem on Newton's method under majorant condition in Riemannian manifolds ⋮ An efficient damped Newton-type algorithm with globalization strategy on Riemannian manifolds ⋮ On the superlinear convergence of Newton's method on Riemannian manifolds ⋮ Damped Newton's method on Riemannian manifolds ⋮ Convergence criteria of Newton's method on Lie groups ⋮ Convergence of Newton's method for sections on Riemannian manifolds ⋮ A robust Kantorovich's theorem on the inexact Newton method with relative residual error tolerance ⋮ A robust semi-local convergence analysis of Newton's method for cone inclusion problems in Banach spaces under affine invariant majorant condition ⋮ Traub-type high order iterative procedures on Riemannian manifolds ⋮ Newton’s method for variational inequality problems: Smale’s point estimate theory under the γ-condition ⋮ Local convergence of Newton's method on Lie groups and uniqueness balls ⋮ Extending the applicability of Newton's method on Lie groups ⋮ Local convergence of Newton's method on the Heisenberg group ⋮ On Newton's method for solving generalized equations

Cites Work

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• On dominating sequence method in the point estimate and Smale's theorem
• A unifying local convergence result for Newton's method in Riemannian manifolds
• Minimizing a differentiable function over a differential manifold
• High order Runge-Kutta methods on manifolds
• Convergence on the iteration of Halley family in weak conditions
• The Newton iteration on Lie groups
• Kantorovich's theorem on Newton's method in Riemannian manifolds
• The geometry of the Newton method on non-compact Lie groups
• The constrained Newton method on a Lie group and the symmetric eigenvalue problem
• The Geometry of Algorithms with Orthogonality Constraints
• Optimization Techniques on Riemannian Manifolds
• Newton's method on Riemannian manifolds: covariant alpha theory
• Newton's method on Riemannian manifolds: Smale's point estimate theory under the γ-condition

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