The Method of Alternating Relaxed Projections for two nonconvex sets

The Method of Alternating Projections (MAP), a classical algorithm for solving feasibility prob- lems, has recently been intensely studied for nonconvex sets. However, intrinsically available are only local convergence results: convergence occurs if the starting point is not too far away from solutions to avoid getting trapped in certain regions. Instead of taking full projection steps, it can be advantageous to underrelax, i.e., to move only part way towards the constraint set, in order to enlarge the regions of convergence. In this paper, we thus systematically study the Method of Alternating Relaxed Projections (MARP) for two (possibly nonconvex) sets. Complementing our recent work on MAP, we es- tablish local linear convergence results for the MARP. Several examples illustrate our analysis

Highly Sensitive Centrality Dependence of Elliptic Flow -- A Novel Signature of the Phase Transition in QCD

Elliptic flow of the hot, dense system which has been created in nucleus-nucleus collisions develops as a response to the initial azimuthal asymmetry of the reaction region. Here it is suggested that the magnitude of this response shows a ``kinky'' dependence on the centrality of collisions for which the system passes through a first-order or rapid transition between quark-gluon plasma and hadronic matter. We have studied the system Pb(158AGeV) on Pb employing a recent version of the transport theoretical approach RQMD and find the conjecture confirmed. The novel phase transition signature may be observable in present and forthcoming experiments at CERN-SPS and at RHIC, the BNL collider.Comment: Version as published in PRL 82 (1999) 2048, title chang