On Berinde’s method for comparing iterative processes

Abstract

In the literature there are several methods for comparing two convergent iterative processes for the same problem. In this note we have in view mostly the one introduced by Berinde in (Fixed Point Theory Appl. 2:97–105, 2004) because it seems to be very successful. In fact, if IP1 and IP2 are two iterative processes converging to the same element, then IP1 is faster than IP2 in the sense of Berinde. The aim of this note is to prove this almost obvious assertion and to discuss briefly several papers that cite the mentioned Berinde’s paper and use his method for comparing iterative processes.

Stability Results and Reckoning Fixed Point Approaches by a Faster Iterative Method with an Application

“…The choice of one iterative method over another is influenced by a few key elements, including speed, stability, and dependence. In recent years, academics have become increasingly interested in iterative algorithms with FPs that depend on data; for further information, see [28][29][30][31].…”