  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.
