Improved monte carlo linear solvers through non-diagonal splitting

Abstract

Fast, but approximate, solutions to linear algebra problems have many potential applications, such as in graph partitioning, pre-conditioning, information retrieval, etc. Monte Carlo techniques appear attractive for such needs. While Monte Carlo linear solvers have a long history, their application has been limited due to slow convergence. Despite the development of techniques to improve their accuracy, current methods suffer from the drawback that they are stochastic realizations of inherently poor iterative methods. The reason for such choices is the need for efficient Monte Carlo implementation, which has restricted the splittings that are considered. However, in this paper we demonstrate that such restrictions are not necessarily required, and that efficient Monte Carlo implementations are possible even with splittings that do not appear amenable to it. © Springer-Verlag 2003.