p-Adic Stability In Linear Algebra

Xavier Caruso (1) , David Roe (2) , Tristan Vaccon (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 University of Calgary

Using the differential precision methods developed previously by the same authors, we study the p-adic stability of standard operations on matrices and vector spaces. We demonstrate that lattice-based methods surpass naive methods in many applications, such as matrix multiplication and sums and intersections of subspaces. We also analyze determinants , characteristic polynomials and LU factorization using these differential methods. We supplement our observations with numerical experiments.

Mots clés: p-adic precision; linear algebra; ultrametric analysis

Domaines: Théorie des nombres [math.NT]; Calcul formel [cs.SC]

Xavier Caruso, David Roe, Tristan Vaccon. p-Adic Stability In Linear Algebra. ISSAC 2015, Jul 2015, Bath, United Kingdom. ⟨10.1145/2755996.2756655⟩. ⟨hal-01164465⟩