Title: Randomized Projection Algorithms for Solving Large Linear Systems.
Abstract: Large data sets common to modern applications has motivated the search for fast and accurate algorithms to solve linear systems. Since direct methods are not feasible for solving many of these problems, iterative methods were developed so that an approximate solution could be obtained with a prescribed degree of accuracy. This allowed the user to control the amount of time and memory allocated to the particular task. These advantages motivated the search of linear system solvers using sampling methods which give a sketch of the original system that lessens the computational burden. Of those methods, randomized iterative methods where the original system would either be stochastically manipulated or sampled became of interest due to the fast convergence and significantly improved running time. This is of particular interest in the context of petascale and exascale computing where the time to perform floating point operations is becoming exponentially less than the time it takes to move the data and communicate the results of the intermediate calculations. In this presentation, the focus will be on randomized projection type methods, presenting some preliminary results using large scale benchmark matrices.