Performance of asynchronous linear iterations with random delays

In this paper we investigate the speedup potential of asynchronous iterative algorithms over their synchronous counterparts for the special case of linear iterations. The space of linear iterations of size two is explored by simulation and analytical methods. We find cases and conditions for high asynchronous speedups. However, averaging asynchronous speedups over the whole set of iteration matrices reveals that the domain of matrices with high speedups is not sizable and that asynchronous iterations perform no better than synchronous ones over the entire convergence space.