Fixed-point iterative linear inverse solver with extended precision

Zhu, Zheyuan; Klein, Andrew B.; Li, Guifang; Pang, Shuo

doi:10.48550/arxiv.2105.02106

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2021

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“…The latter approach was used to apply overlapping block-Jacobi preconditioners in the Generalized Minimal RESidual (GMRES) iterative solver [20] with bitslicing for increasing precision. Inner-outer iterations [24]- [26] have been considered for dense systems, where analog arrays were used for the inner solver while iterative refinement was used as an outer solver in the digital space.…”

Section: Introductionmentioning

confidence: 99%

Solving sparse linear systems with approximate inverse preconditioners on analog devices

Kalantzis¹,

Gupta²,

Horesh³

et al. 2021

Preprint

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Sparse linear system solvers are computationally expensive kernels that lie at the heart of numerous applications. This paper proposes a preconditioning framework that combines approximate inverses with stationary iterations 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.

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Section: Introductionmentioning

confidence: 99%