Correcting matrix products over the ring of integers

07/24/2023

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by   Yu-Lun Wu, et al.

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Let A, B, and C be three n× 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(√(k)n^2+k^2n) operations. Let α be the largest integers in A, B, and C. The largest value involved in the computation is of O(n^3α^2).