Kantorovich's theorem on Newton's method in Riemannian Manifolds
Journal of Complexity
An adaptive version of a fourth-order iterative method for quadratic equations
Journal of Computational and Applied Mathematics - Special issue: The international conference on computational methods in sciences and engineering 2004
A Unifying Local Convergence Result for Newton's Method in Riemannian Manifolds
Foundations of Computational Mathematics
Optimization Algorithms on Matrix Manifolds
Optimization Algorithms on Matrix Manifolds
Journal of Complexity - Festschrift for the 70th birthday of Arnold Schönhage
On a characterization of some Newton-like methods of R-order at least three
Journal of Computational and Applied Mathematics
An extension of Gander's result for quadratic equations
Journal of Computational and Applied Mathematics
Third-order iterative methods with applications to Hammerstein equations: A unified approach
Journal of Computational and Applied Mathematics
Riemannian Newton Method for the Multivariate Eigenvalue Problem
SIAM Journal on Matrix Analysis and Applications
Hi-index | 7.29 |
One of the most studied problems in numerical analysis is the approximation of nonlinear equations using iterative methods. In the past years, attention has been paid in studying Newton's method on manifolds. In this paper, we generalize this study by considering a general class of third-order iterative methods. A characterization of the convergence under Kantorovich type conditions and optimal error estimates is found.