Some Newton-like methods with sharper error estimates for solving operator equations in Banach spaces

Fixexd point theory and applications

DR Sahu¹  Vipin Kumar Singh¹  Krishna Kumar Singh¹ 

[1] Department of Mathematics, Faculty of Science, Banaras Hindu University, Varanasi, India

关键词: Banach contraction theorem;    fixed point;    Fréchet derivative;    Newton's method;    nonlinear operator equations;    quasi-contraction;    S-operator.;   

DOI  :  10.1186/1687-1812-2012-78

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

It is well known that the rate of convergence of S-iteration process introduced by Agarwal et al. (pp. 61-79) is faster than Picard iteration process for contraction operators. Following the ideas of S-iteration process, we introduce some Newton-like algorithms to solve the non-linear operator equation in Banach space setting. We study the semi-local as well as local convergence analysis of our algorithms. The rate of convergence of our algorithms are faster than the modified Newton method. Mathematics Subject Classification 2010: 49M15; 65K10; 47H10.

【 授权许可】

CC BY