Implementing Asynchronous Linear Solvers Using Non-Uniform Distributions

Asynchronous iterative methods present a mechanism to improve the performance of algorithms for highly parallel computational platforms by removing the overhead associated with synchronization among computing elements. This paper considers a class of asynchronous iterative linear system solvers that employ randomization to determine the component update orders, specifically focusing on the effects of drawing the order from non-uniform distributions. Results from shared-memory experiments with a two-dimensional finite-difference discrete Laplacian problem show that using distributions favoring the selection of components with a larger contribution to the residual may lead to faster convergence than selecting uniformly. Multiple implementations of the randomized asynchronous linear system solvers are considered and tested with various distributions and parameters. In the best case of parameter choices, average times for the normal and exponential distributions were, respectively, 13.3% and 17.3% faster than the performance with a uniform distribution, and were able to converge in approximately 10% fewer iterations than traditional stationary solvers