Fixed-point iterative linear inverse solver with extended precision

TL;DR

This paper demonstrates that fixed-point processors can effectively perform iterative linear system solving with high precision by using residual iteration, enabling energy-efficient computation without sacrificing accuracy.

Contribution

It introduces a method to achieve high-precision solutions on fixed-point processors through residual iteration, expanding their applicability to linear inverse problems.

Findings

Fixed-point iterative solver can match floating-point convergence rates.

Residual iteration enables high-precision solutions beyond native fixed-point limits.

Power-efficient analog computing devices can be used for accurate linear system solving.

Abstract

Solving linear systems is a ubiquitous task in science and engineering. Because directly inverting a large-scale linear system can be computationally expensive, iterative algorithms are often used to numerically find the inverse. To accommodate the dynamic range and precision requirements, these iterative algorithms are often carried out on floating-point processing units. Low-precision, fixed-point processors require only a fraction of the energy per operation consumed by their floating-point counterparts, yet their current usages exclude iterative solvers due to the computational errors arising from fixed-point arithmetic. In this work, we show that for a simple iterative algorithm, such as Richardson iteration, using a fixed-point processor can provide the same rate of convergence and achieve high-precision solutions beyond its native precision limit when combined with residual iteration. These results indicate that power-efficient computing platform consisting of analog computing devices can be used to solve a broad range of problems without compromising the speed or precision.