LU factorization with errors

Jean-Guillaume Dumas (1) , Joris van der Hoeven (2) , Clément Pernet (1) , Daniel S. Roche (3)

1 CASC - Calcul Algébrique et Symbolique, Sécurité, Systèmes Complexes, Codes et Cryptologie
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
3 United States Naval Academy

We present new algorithms to detect and correct errors in the lower-upper factorization of a matrix, or the triangular linear system solution, over an arbitrary field. Our main algorithms do not require any additional information or encoding other than the original inputs and the erroneous output. Their running time is softly linear in the dimension times the number of errors when there are few errors, smoothly growing to the cost of fast matrix multiplication as the number of errors increases. We also present applications to general linear system solving.

Domaines: Calcul formel [cs.SC]; Théorie de l'information [cs.IT]; Algorithme et structure de données [cs.DS]; Logiciel mathématique [cs.MS]

Jean-Guillaume Dumas, Joris van der Hoeven, Clément Pernet, Daniel S. Roche. LU factorization with errors. International Symposium on Symbolic and Algebraic Computation - ISSAC'19, Jul 2019, Beijing, China. pp.131-138, ⟨10.1145/3326229.3326244⟩. ⟨hal-01997592⟩