An algorithm with long steps for the simultaneous block projections approach for the linear feasibility problem

The main issue which is discussed in this paper is an improved step sizing policy for simultaneous projection methods. Experimental results reveal that the conventional step size obtained as the convex combination of distinct projections made simultaneously, deteriorate the performance of the algorithms severely. We consider a longer step size based on the acceleration techniques which have been discussed recently in the literature. Utilization of this step size improves the performance of the simultaneous block projections algorithm significantly so that the simultaneous algorithm performs better than the successive block projections algorithm, which is not quite the case with the conventional short-step methods. Although we have considered the linear feasibility problem convergence results are applicable to the covex feasibility problem as well.