A convergence analysis of an iterative algorithm of order \(1.839\ldots\) under weak assumptions

Journal of Numerical Analysis and Approximation Theory

Ioannis K. Argyros¹ 

[1] Cameron University, Lawton, United States;

关键词: Banach space;    majorizing sequence;    Halley method;    Euler-Chebyshev method;    divided differences of order one and two;    Fréchet-derivative;   

DOI  :  

来源: DOAJ

【 摘 要 】

We provide new and weaker sufficient local and semilocal conditions for the convergence of a certain iterative method of order 1.839\(\ldots\) to a solution of an equation in a Banach space. The new idea is to use center-Lipschitz/Lipschitz conditions instead of just Lipschitz conditions on the divided differences of the operator involved. This way we obtain finer error bounds and a better information on the location of the solution under weaker assumptions than before.

【 授权许可】

Unknown