Computing the inertia of Bézout and Hankel matrices
type: Item
instance of: scholarly article
title: Computing the inertia of Bézout and Hankel matrices
zbMATH Open document ID: 0766.65035
DOI: 10.1007/BF02575814
author: L. Gemignani
published in: Calcolo
publication date: 1993-01-19T00:00:00Z
review text: This paper is concerned with a sequential algorithm for computing the diagonal matrix \(D\) in the block \(LDL^ T\) factorization which evaluates the inertia of real Hankel and Bézout matrices \(A\) (i.e., the numbers of eigenvalues of \(A\) with positive, zero, and negative real parts). The algorithm is \(O(n\log^ 3n)\), better than any other known sequential algorithm for this problem. This improvement stems from relations between the polynomial remainder sequences generated by the Euclidean scheme when applied to two polynomials, and by Bézout and Hankel matrix computations developed by \textit{D. Bini}, the author, and \textit{V. Pan} [Improved parallel computations with matrices and polynomials; Proc. 18th EATCS International Colloquium on Automata, Languages and Programming, Lect. Notes Comput. Sci. 510 (Springer 1991)].
reviewed by: Erwin O. Kreyszig
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 98937
zbMATH Keywords: block factorization
zbMATH Keywords: Euclidean scheme
zbMATH Keywords: sequential algorithm
zbMATH Keywords: diagonal matrix
zbMATH Keywords: inertia
zbMATH Keywords: Hankel and Bézout matrices
zbMATH Keywords: numbers of eigenvalues
MaRDI profile type: Publication
cites work: Q4036590
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description: scientific article; zbMATH DE number 98937