Skip to Main content Skip to Navigation
Conference papers

Certificates for triangular equivalence and rank profiles

Abstract : In 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.
Document type :
Conference papers
Complete list of metadata

Cited literature [16 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01466093
Contributor : Clément Pernet <>
Submitted on : Sunday, October 20, 2019 - 4:14:13 PM
Last modification on : Thursday, November 19, 2020 - 1:02:10 PM
Long-term archiving on: : Tuesday, January 21, 2020 - 1:10:24 PM

Files

rpm_certificate.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Jean-Guillaume Dumas, David Lucas, Clément Pernet. Certificates for triangular equivalence and rank profiles. ACM International Symposium on Symbolic and Algebraic Computations - ISSAC'17, Jul 2017, Kaiserslautern, Germany. pp.133-140, ⟨10.1145/3087604.3087609⟩. ⟨hal-01466093v2⟩

Share

Metrics

Record views

331

Files downloads

756