Expanding the applicability of Newton鈥檚 method using Smale鈥檚 -theory
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- 作者：Ioannis K. Argyros ; Sa茂d Hilout ; Sanjay K. Khattri
- 关键词：Newton&rsquo ; s method ; Banach space ; Semi-local convergence ; Smale&rsquo ; s 伪伪-theory ; Fré ; chet-derivative
- 刊名：Journal of Computational and Applied Mathematics
- 出版年：1 May, 2014
- 年：2014
- 卷：261
- 期：Complete
- 页码：183-200
- 全文大小：518 K
文摘
We present a tighter convergence analysis than earlier studies such as in Cianciaruso (2007), Guo (2007), Shen and Li (2010), Smale (1986, 1987), Wang and Zhao (1995), Wang (1999), Wang and Han (1990) of Newton鈥檚 method using Smale鈥檚 -theory by introducing the notion of the center -condition. In particular, in the semilocal convergence case we show that if the center -condition is smaller than the -condition, then the new majorizing sequence is tighter than the old majorizing sequence. The new convergence criteria are weaker than the older convergence criteria. Furthermore, in the local convergence case, we obtain a larger radius of convergence and tighter error estimates on the distances involved. These improvements are obtained under the same computational cost. Numerical examples and applications are also provided in this study to show that the older results cannot apply but the new results apply to solve equations.