The theory and applications of Iteration Methods is a very fast-developing field of numerical
analysis and computer methods. The second edition is completely updated and continues to …

We provide a local convergence analysis for Newton's method under a weak majorant
condition in a Banach space setting. Our results provide under the same information a larger …

One kind of the L-average Lipschitz condition is introduced to covariant derivatives of
sections on Riemannian manifolds. A convergence criterion of Newton's method and the …

The notions of Lipschitz conditions with L average are introduced to the study of
convergence analysis of Gauss–Newton's method for singular systems of equations. Unified …

In this paper, we consider Newton's method for solving a generalized equation. We show
that under strong regularity of the equation and on the condition that the starting point …

We extend the applicability of the Gauss–Newton method for solving singular systems of
equations under the notions of average Lipschitz–type conditions introduced recently in Li et …

Robinson's generalized Newton's method for nonlinear functions with values in a cone is
extended to mappings on Riemannian manifolds with values in a cone. When ${\cal D} f …

We present a local convergence analysis of the proximal Gauss–Newton method for solving
penalized nonlinear least squares problems in a Hilbert space setting. Using more precise …

With the classical assumptions on f, a convergence criterion of Newton's method
(independent of affine connections) to find zeros of a mapping f from a Lie group to its Lie …

We present a local convergence of the combined Newton-Kurchatov method for solving
Banach space valued equations. The convergence criteria involve derivatives until the …