Random matrices over a DVR and LU factorization. (November 2015)

• Record Type: Journal Article
• Authors: Caruso, Xavier
• Is Part Of: Journal of symbolic computation. Volume 71(2016)
• Page Start: 98
• Page End: 123
• Publication Date: 2015-11
• Subjects: p-adic precision -- LU factorization; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2014.12.001
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Let R be a discrete valuation ring (DVR) and K be its fraction field. If M is a matrix over R admitting an LU decomposition, it could happen that the entries of the factors L and U do not lie in R, but just in K . Having a good control on the valuations of these entries is very important for algorithmic applications. In the paper, we prove that on average these valuations are not too large and explain how one can apply this result to provide an efficient algorithm computing a basis of a coherent sheaf over A K 1 from the knowledge of its stalks.