Correcting matrix products over the ring of integers

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(kn2+k2n) operations. Let α be the largest absolute val...

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Bibliographic Details
Published inInformation processing letters Vol. 186; p. 106496
Main Authors Wu, Yu-Lun, Wang, Hung-Lung
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.08.2024
Subjects
Algorithms
Certifying algorithm
Correction
Design of algorithms
Matrix multiplication
Algorithms
Matrix multiplication
Design of algorithms
Certifying algorithm
Correction
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Summary: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(kn2+k2n) operations. Let α be the largest absolute value of an entry in A, B, and C. The integers involved in the computation are of O(n3α2). •A simple combinatorial algorithm for correcting integer matrix products.•Detecting erroneous entries by combinatorial group testing.•Integers used in the computation are polynomial bounded in the input value and size.
ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2024.106496