Fast fraction-free triangularization of Bézoutians with applications to sub-resultant chain computation
type: Item
instance of: scholarly article
title: Fast fraction-free triangularization of Bézoutians with applications to sub-resultant chain computation
zbMATH Open document ID: 0937.65031
DOI: 10.1016/S0024-3795(98)10075-7
author: L. Gemignani
author: Dario A. Bini
published in: Linear Algebra and its Applications
publication date: 1999-11-28T00:00:00Z
review text: It is shown that a variant of Gaussian elimination can be applied to factor a permuted Bézoutian and keep the structural properties of the Schur complements unchanged. This process provides a fast division-free algorithm for computing a polynomial remainder sequence of two polynomials. It is pointed out that the same result holds for polynomials having coefficients over a general integral domain. A strategy, that leads to a method for computing the \(LDL^T\) factorization of a permuted Bézoutian that is useful in the solution of root localization problems, is presented.
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 12Y05
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 1371008
zbMATH Keywords: Gaussian elimination for Bézoutians
zbMATH Keywords: integer LU factorization
zbMATH Keywords: polynomial matrices
zbMATH Keywords: Schur complements
zbMATH Keywords: division-free algorithm
zbMATH Keywords: root localization problems
reviewed by: R. P. Tewarson
MaRDI profile type: Publication
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Wikidata QID: Q127740442
description: scientific article; zbMATH DE number 1371008