Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4640266 | Journal of Computational and Applied Mathematics | 2011 | 8 Pages |
Abstract
A local convergence analysis of Newton’s method for solving nonlinear equations, under a majorant condition, is presented in this paper. Without assuming convexity of the derivative of the majorant function, which relaxes the Lipschitz condition on the operator under consideration, convergence, the biggest range for uniqueness of the solution, the optimal convergence radius and results on the convergence rate are established. Besides, two special cases of the general theory are presented as applications.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
O.P. Ferreira,