Correcting matrix products over the ring of integers

Yu-Lun Wu; Hung-Lung Wang

doi:10.1016/j.ipl.2024.106496

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arXiv · 2307.12513

Correcting matrix products over the ring of integers

Yu-Lun Wu·Hung-Lung Wang

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Abstract

Let $A$, $B$, and $C$ be three $n\times n$ matrices. We investigate the problem of verifying whether $AB=C$ over the ring of integers and finding the correct product $AB$. Given that $C$ is different from $AB$ by at most $k$ entries, we propose an algorithm that uses $O(\sqrt{k}n^2+k^2n)$ operations. Let $\alpha$ be the largest absolute value of an entry in $A$, $B$, and $C$. The integers involved in the computation are of $O(n^3\alpha^2)$.

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Yu-Lun Wu, Hung-Lung Wang. 2023-07-24. Correcting matrix products over the ring of integers. https://doi.org/10.1016/j.ipl.2024.106496

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