PittsburghV1, France, Analysis, bibRecord, 000024

Characteristic polynomials of p-adic matrices

Identifieur interne : 000024 ( France/Analysis ); précédent : 000023; suivant : 000025

Characteristic polynomials of p-adic matrices

Auteurs : Xavier Caruso [France] ; David Roe [États-Unis] ; Tristan Vaccon [France]

Source :

RBID : Hal:hal-01458027

English descriptors

mix :
- Algorithms, characteristic polynomial, eigenvalue, p-adic precision.

Abstract

We analyze the precision of the characteristic polynomial of an n×n p-adic matrix A using differential precision methods developed previously. When A is integral with precision O(p^N), we give a criterion (checkable in time O˜(n^omega)) for χ(A) to have precision exactly O(p^N). We also give a O˜(n^3) algorithm for determining the optimal precision when the criterion is not satisfied, and give examples when the precision is larger than O(p^N).

Url:

https://hal.archives-ouvertes.fr/hal-01458027

Affiliations:

Links toward previous steps (curation, corpus...)

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Links to Exploration step

Hal:hal-01458027

Le document en format XML

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<front><div type="abstract" xml:lang="en">We analyze the precision of the characteristic polynomial of an n×n p-adic matrix A using differential precision methods developed previously. When A is integral with precision O(p^N), we give a criterion (checkable in time O˜(n^omega)) for χ(A) to have precision exactly O(p^N). We also give a O˜(n^3) algorithm for determining the optimal precision when the criterion is not satisfied, and give examples when the precision is larger than O(p^N).</div>
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Characteristic polynomials of p-adic matrices

Characteristic polynomials of p-adic matrices

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