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

Ioannis Argyros, Santhosh George
2018 Mathematics  
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
more » ... region containing the iterates as before and consequently also a tighter convergence analysis.
doi:10.3390/math6110233 fatcat:co7dvgg6l5fbfcnsjlak3v4yji