A Sampling Kaczmarz-Motzkin Algorithm for Linear Feasibility
  We combine two iterative algorithms for solving large-scale systems of linear inequalities, the relaxation method of Agmon, Motzkin et al. and the randomized Kaczmarz method. In doing so, we obtain a family of algorithms that generalize and extend both techniques. We prove several convergence results, and our computational experiments show our algorithms often outperform the original methods. 
Jesus De Loera, Jamie Haddock, Deanna Needell
math.OC