  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.
