Improved convergence of Steffensen's method for approximating fixed points of operators in Banach space

摘要

We present a new local as well as a semilocal convergence analysis for Steffensen's method in order to locate fixed points of operators on a Banach space setting. Using more precise majorizing sequences we show under the same or less computational cost that our convergence criteria can be weaker than in earlier studies such as cite{1,2,3,4,5,6,7,8,9,10,11,12,13}, cite{21,22}. Numerical examples are provided to illustrate the theoretical results.