Solving sparse linear systems with approximate inverse preconditioners on analog devices

TL;DR

This paper introduces a hybrid digital-analog approach to solve sparse linear systems more efficiently, achieving significant speedups with minimal impact on accuracy by leveraging analog crossbar accelerators.

Contribution

It presents a novel preconditioning framework that combines digital and analog hardware to accelerate sparse linear system solving.

Findings

Achieves an order of magnitude speedup in solving sparse systems

Maintains convergence quality despite analog hardware noise

Demonstrates effectiveness through simulation results

Abstract

Sparse linear system solvers are computationally expensive kernels that lie at the heart of numerous applications. This paper proposes a flexible preconditioning framework 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.