Unified Semi-Local Convergence for k—Step Iterative Methods with Flexible and Frozen Linear Operator

Mathematics

IoannisK. Argyros¹  Santhosh George² 

[1] Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA;Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Mangalore 575 025, India;

关键词: Banach space;    k-step method;    semi-local convergence;    Lipschitz conditions;   

DOI  :  10.3390/math6110233

来源: DOAJ

【 摘 要 】

The aim of this article is to present a unified semi-local convergence analysis for a k-step iterative method containing the inverse of a flexible and frozen linear operator for Banach space valued operators. Special choices of the linear operator reduce the method to the Newton-type, Newton’s, or Stirling’s, or Steffensen’s, or other methods. The analysis is based on center, as well as Lipschitz conditions and our idea of the restricted convergence region. This idea defines an at least as small region containing the iterates as before and consequently also a tighter convergence analysis.

【 授权许可】

Unknown