Newton method under weak Lipschitz continuous derivative in Banach spaces

Authors:
Zhengda Huang
Affiliations:
Department of Mathematics, XiXi Campus, Zhejiang University, Hangzhou 310028, China
Venue:
Applied Mathematics and Computation
Year:
2003

Citing 8
Cited 2

A method for finding sharp error bounds for newton's method under the kantorovic assumptions

Numerische Mathematik
On a theorem of S. Smale about Newton's method for analytic mappings

Applied Mathematics Letters
A note on the Kantorovich theorem for Newton iteration

Journal of Computational and Applied Mathematics
A new semilocal convergence theorem for Newton's method

Journal of Computational and Applied Mathematics
Convergence of Newton's method and inverse function theorem in Banach space

Mathematics of Computation
On Newton's method under mild differentiability conditions and applications

Applied Mathematics and Computation
Iterative solution of nonlinear equations in several variables

Iterative solution of nonlinear equations in several variables
A new semilocal convergence theorem for Newton's method in Banach space using hypotheses on the second Fréchet-derivative

Journal of Computational and Applied Mathematics

Kantorovich's majorants principle for Newton's method

Computational Optimization and Applications
Improved local convergence of Newton's method under weak majorant condition

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.48

Visualization

Abstract

In the present paper, a relax Kantorovich-type condition to guarantee the convergence of Newton method with order 2 in Banach space is obtained, which takes the well-known Kantorovich and Smale conditions as its special cases. The relations between the new condition and the old ones are also studied.