Inexact Newton's method to nonlinear functions with values in a cone
Numerical Analysis
2016-04-22 v2
Abstract
The problem of finding a solution of nonlinear inclusion problems in Banach space is considered in this paper. Using convex optimization techniques introduced by Robinson (Numer. Math., Vol. 19, 1972, pp. 341-347), a robust convergence theorem for inexact Newton's method is proved. As an application, an affine invariant version of Kantorovich's theorem and Smale's \alpha-theorem for inexact Newton's method is obtained.
Keywords
Cite
@article{arxiv.1510.01947,
title = {Inexact Newton's method to nonlinear functions with values in a cone},
author = {O. P. Ferreira and G. N. Silva},
journal= {arXiv preprint arXiv:1510.01947},
year = {2016}
}
Comments
15 pages, 0 figure. arXiv admin note: text overlap with arXiv:1403.2462