"Convergence of a continuous analog of Newton's method for
solving nonlinear equations" Zhanlav T., Chuluunbaatar O. |
The influence of the parameter in the continuous analog of Newton's method (CANM) on the convergence and on the convergence rate is studied. A τ-region of convergence of CANM for both scalar equations and equations in a Banach space is obtained. Some almost optimal choices of the parameter are proposed. It is also shown that the well-known higher order convergent iterative methods lead to the CANM with an almost optimal parameter. Several sufficient convergence conditions for these methods are obtained. Keywords: iterative methods, rate of convergence, Newton-type methods, nonlinear equations |
Zhanlav T., Academician, e-mail: zhanlav@yahoo.com
- Department of Applied Mathematics, National University of Mongolia,
Ulan-Bator, Mongolia; Chuluunbaatar O., Senior Scientist, e-mail: chuka@jinr.ru = Joint Institute for Nuclear Research, Dubna, 141980 Moscow Region, Russia |