Papers › A circumcentered-reflection method for finding common fixed points of firmly...
A circumcentered-reflection method for finding common fixed points of firmly nonexpansive operators
Reza Arefidamghani, Roger Behling, Alfredo N. Iusem, Luiz-Rafael Santos
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
The circumcentered-reflection method (CRM) has been recently proposed as a methodology for accelerating several algorithms for solving the Convex Feasibility Problem (CFP), equivalent to finding a common fixed-point of the orthogonal projections onto a finite number of closed and convex sets. In this paper, we apply CRM to the more general Fixed Point Problem (denoted as FPP), consisting of finding a common fixed-point of operators belonging to a larger family of operators, namely firmly nonexpansive operators. We prove than in this setting, CRM is globally convergent to a common fixed-point (supposing at least one exists). We also establish linear convergence of the sequence generated by CRM applied to FPP, under a not too demanding error bound assumption, and provide an estimate of the asymptotic constant. We provide solid numerical evidence of the superiority of CRM when compared to the classical Parallel Projections Method (PPM). Additionally, we present certain results of convex combination of orthogonal projections, of some interest on its own.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections