Deteriorating Convergence for Asynchronous Methods on Linear Least Squares Problems

. A block iterative method is used for solving linear least squares problems. The subproblems are solved asynchronously on a distributed memory multiprocessor. It is observed that an increased number of processors results in deteriorating rate of convergence. This deteriorating convergence is illustrated by numerical experiments. The deterioration of the convergence can be explained by contamination of the residual. Our purpose is to show that the residual is contaminated by old information. The issues investigated here are the effect of the number of processors, the role of essential neighbors, and synchronization. The characterization of old information remains an open problem. 1 Introduction In this paper, a block iterative method is used for solving sparse linear least squares problems. A general framework for this method is introduced by Dennis and Steihaug [4], and the preliminary tests in [4] indicate that this method leads quickly to cheap solutions of limited accura..