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Certificates for triangular equivalence and rank profiles

By Jean-Guillaume Dumas, David Lucas and Clément Pernet

Abstract

International audienceIn this paper, we give novel certificates for triangular equivalence and rank profiles. These certificates enable to verify the row or column rank profiles or the whole rank profile matrix faster than recomputing them, with a negligible overall overhead. We first provide quadratic time and space non-interactive certificates saving the logarithmic factors of previously known ones. Then we propose interactive certificates for the same problems whose Monte Carlo verification complexity requires a small constant number of matrix-vector multiplications, a linear space, and a linear number of extra field operations. As an application we also give an interactive protocol, certifying the determinant of dense matrices, faster than the best previously known one

Topics: [INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC]
Publisher: 'Association for Computing Machinery (ACM)'
Year: 2017
DOI identifier: 10.1145/3087604.3087609
OAI identifier: oai:HAL:hal-01466093v2
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