A Distributed Solver for Dense Linear Feasibility Systems

The aim of this paper is to present a new hybrid solver for linear feasibility systems that uses a block-parallel scheme combined with a new variable weight projection operator which takes into account the distances to the semi spaces onto which it projects. The solver can tackle very large, dense, systems. The results of our study show that a specialized variant of the solver is more efficient at solving a certain class of dense systems in terms of resources than other variants. Furthermore, we will also show results that suggest that the distribution scheme does not greatly affect the number of required iterations for a solution to be reached.