Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4635202 | Applied Mathematics and Computation | 2007 | 7 Pages |
Abstract
This paper presents the new convergence analysis for the Newton-like method proposed by [Xinyuan Wu, A new continuation Newton-like method and its deformation, Appl. Math. Comput. 112 (2000) 75-78.] Compared with the original version of the convergence analysis, the restriction imposed on fâ³(x) is removed thoroughly. In order to guarantee the quadratic convergence of the Newton-like method, it is suffices to suppose that fâ²(xâ)Â â Â 0 and fâ²(x) is local Lipschitz near xâ, where xâ is a solution of nonlinear equation f(x)Â =Â 0. Moreover, some comments are given with examples for the Newton-like method, in comparison with Newton's method. It can be concluded that the new algorithm is more feasible, effective than Newton's method. In particularly, when it happens that, the derivative of the function f(x) at an iterate is singular or almost singular, the Newton-like method is vast superior to the classical Newton method. The numerical results of the paper strongly support the conclusion.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Xinyuan Wu,