Expanding the applicability of Newton's method using Smale's α-theory

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:261

Article

Argyros, Ioannis K.¹  Hilout, Said²  Khattri, Sanjay K.³ 

[1] Cameron Univ, Dept Math Sci, Lawton, OK 73505 USA

[2] Univ Quebec Montreal, Dept Sci Terre & Atmosohere, Montreal, PQ H3C 3P8, Canada

[3] Stord Haugesund Univ Coll, Haugesund, Norway

关键词: Newton's method;    Banach space;    Semi-local convergence;    Smale's alpha-theory;    Frechet-derivative;   

DOI  :  10.1016/j.cam.2013.10.054

来源: Elsevier

【 摘 要 】

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's method using Smale's alpha-theory by introducing the notion of the center gamma(0)-condition. In particular, in the semilocal convergence case we show that if the center gamma(0)-condition is smaller than the gamma-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. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free