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DOE OSTI · 2570779

Memristive linear algebra

Lin, John [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0009000228555086)·Barrows, Frank Patrick [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000193079771)·Caravelli, Francesco [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000179643030)
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Abstract

The advent of memristive devices offers a promising avenue for efficient and scalable analog computing, particularly for linear algebra operations essential in various scientific and engineering applications. This paper investigates the potential of memristive crossbars in implementing matrix inversion algorithms. We explore both static and dynamic approaches, emphasizing the advantages of analog and in-memory computing for matrix operations beyond multiplication. In particular, we demonstrate that the electrical properties of memristive crossbars uniquely suit them for the evolution of a family of matrix exponentials, which can be exploited for the efficient computation of matrix inverses and online solutions for linear problems. Our results demonstrate that memristive arrays can reduce computational complexity. We also study power consumption and show a tradeoff between precision and energy. Furthermore, we address the challenges of device variability, precision, and scalability, providing insights into the practical implementation of these algorithms.

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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS97 MATHEMATICS AND COMPUTING

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Lin, John [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0009000228555086), Barrows, Frank Patrick [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000193079771), Caravelli, Francesco [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000179643030). 2025-06-10. Memristive linear algebra. https://doi.org/10.1103/physrevresearch.7.023241

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