Extending the applicability of Newton’s method for k-Fréchet differentiable operators in Banach spaces
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摘要
We extend the applicability of Newton’s method for k-Fréchet differentiable operators in a Banach space setting by using a more flexible way of computing upper bounds on the inverses of the operators involved. In particular, we improve and extend the recent works by Ezquerro et al. (2012, 2013) [13,15]. Moreover, we illustrate our study with some numerical examples involving Hammerstein integral equations.
论文关键词：Newton’s method,Semilocal convergence,The Newton–Kantorovich theorem,Majorizing sequence,A priori error estimates,Hammerstein integral equation
论文评审过程：Available online 9 March 2014.
论文官网地址：https://doi.org/10.1016/j.amc.2014.02.046
