Asynchronous Methods and Least Squares: An Example of Deteriorating Convergence

Abstract

We use block iterative methods for solving linear least squares problems. The subproblems are solved asynchronously on a distributed memory multiprocessor. It is observed that increased number of processors results in deteriorating convergence. We illustrate the deteriorating convergence by some numerical experiments. The deterioration of the convergence can be explained by contamination of the residual. The residual is contaminated by old information. Our purpose is to reduce the effect of old information. The issues investigated here are the effect of the number of processors, the role of essential neighbors [8] and heterogeneous processors. We include two heuristics to identify the information to be discarded and reduce the effect of old information: a relaxation factor and synchronization. The characterization of old information remains as an open problem. 1 Introduction In this paper we use block iterative method for solving sparse linear least squares problems. A general framewo..