Geometric optimization methods for adaptive filtering
Geometric optimization methods for adaptive filtering
Complexity and real computation
Complexity and real computation
The Geometry of Algorithms with Orthogonality Constraints
SIAM Journal on Matrix Analysis and Applications
Convergence of Newton's method and inverse function theorem in Banach space
Mathematics of Computation
Kantorovich's theorem on Newton's method in Riemannian Manifolds
Journal of Complexity
Newton's method for sections on Riemannian manifolds: Generalized covariant α-theory
Journal of Complexity
Gauss---Newton method for convex composite optimizations on Riemannian manifolds
Journal of Global Optimization
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This paper is concerned with the problem of the uniqueness of singular points of vector fields on Riemannian manifolds. The radii of the uniqueness balls of the singular points of vector fields are estimated under the assumption that the vector fields satisfy the γ-condition, and the results due to Wang and Han in [Criterion α and Newton's method under weak conditions, Chinese J. Numer. Appl. Math. 19(2) (1997) 96-105] are extended. Moreover, applications to analytic vector fields are given.