Fixed-point iterative linear inverse solver with extended precision

Solving linear systems, often accomplished by iterative algorithms, is a ubiquitous task in science and engineering. To accommodate the dynamic range and precision requirements, these iterative solvers are carried out on floating-point processing units, which are not efficient in handling large-scale matrix multiplications and inversions. Low-precision, fixed-point digital or analog processors consume only a fraction of the energy per operation than their floating-point counterparts, yet their current usages exclude iterative solvers due to the cumulative 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 convergence rate and achieve solutions beyond its native precision when combined with residual iteration. These results indicate that power-efficient computing platforms consisting of analog computing devices can be used to solve a broad range of problems without compromising the speed or precision.