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Mathematics > Optimization and Control

arXiv:1812.00958 (math)
[Submitted on 3 Dec 2018 (v1), last revised 4 Mar 2019 (this version, v4)]

Title:On Berinde's method for comparing iterative processes

Authors:C. Zalinescu
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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 [Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators, Fixed Point Theory Appl. 2004, no. 2, 97--105] 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.
Comments: 10 pages; new references are added
Subjects: Optimization and Control (math.OC)
Cite as: arXiv:1812.00958 [math.OC]
  (or arXiv:1812.00958v4 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.1812.00958

Submission history

From: Constantin Zalinescu [view email]
[v1] Mon, 3 Dec 2018 18:27:10 UTC (8 KB)
[v2] Wed, 12 Dec 2018 16:19:25 UTC (9 KB)
[v3] Sun, 23 Dec 2018 05:44:33 UTC (9 KB)
[v4] Mon, 4 Mar 2019 07:21:56 UTC (11 KB)
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