Solving sparse linear systems with approximate inverse preconditioners on analog devices

Abstract

Sparse linear system solvers are computationally expensive kernels that lie at the heart of numerous applications. This paper proposes a preconditioning framework that combines approximate inverses with stationary iterations to substantially reduce the time and energy requirements of this task by utilizing a hybrid architecture that combines conventional digital microprocessors with analog crossbar array accelerators. Our analysis and experiments with a simulator for analog hardware demonstrate that an order of magnitude speedup is readily attainable without much impact on convergence, despite the noise in analog computations.