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arXiv · 1506.05644

p-Adic Stability In Linear Algebra

Xavier Caruso·David Roe·Tristan Vaccon
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Abstract

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.

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Xavier Caruso, David Roe, Tristan Vaccon. 2015-06-18. p-Adic Stability In Linear Algebra. https://doi.org/10.1145/2755996.2756655

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