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  1. Abstract 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. 
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    Free, publicly-accessible full text available December 1, 2024
  2. Photonic computing has potential advantages in speed and energy consumption yet is subject to inaccuracy due to the limited equivalent bitwidth of the analog signal. In this Letter, we demonstrate a configurable, fixed-point coherent photonic iterative solver for numerical eigenvalue problems using shifted inverse iteration. The photonic primitive can accommodate arbitrarily sized sparse matrix–vector multiplication and is deployed to solve eigenmodes in a photonic waveguide structure. The photonic iterative eigensolver does not accumulate errors from each iteration, providing a path toward implementing scientific computing applications on photonic primitives.

     
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  3. Computational imaging systems with embedded processing have potential advantages in power consumption, computing speed, and cost. However, common processors in embedded vision systems have limited computing capacity and low level of parallelism. The widely used iterative algorithms for image reconstruction rely on floating-point processors to ensure calculation precision, which require more computing resources than fixed-point processors. Here we present a regularized Landweber fixed-point iterative solver for image reconstruction, implemented on a field programmable gated array (FPGA). Compared with floating-point embedded uniprocessors, iterative solvers implemented on the fixed-point FPGA gain 1 to 2 orders of magnitude acceleration, while achieving the same reconstruction accuracy in comparable number of effective iterations. Specifically, we have demonstrated the proposed fixed-point iterative solver in fiber borescope image reconstruction, successfully correcting the artifacts introduced by the lenses and fiber bundle.

     
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