Cholesky-like factorizations of skew-symmetric matrices
type: Item
instance of: scholarly article
title: Cholesky-like factorizations of skew-symmetric matrices
zbMATH Open document ID: 0963.65033
author: P. Benner
author: Ralph Byers
author: Heike Faßbender
author: Volker Mehrmann
author: David S. Watkins
publication date: 2000-11-30T00:00:00Z
full work available at URL: https://eudml.org/doc/121038
full work available at URL: pp85-93.html
full work available at URL: pp93A.html
review text: The authors present a stable \(O(n^3)\) algorithm for computing \(R\) in the Cholesky-like factorization \(B= R^TJR\) of some skew-symmetric \(2n\times 2n\) matrix \(B\), where \(R\) is a permuted triangular matrix and \(J\) has the form \[ J= \left[\begin{matrix} O & I_n\\ -I_n & 0\end{matrix}\right]. \] Cholesky-like factorizations of skew-symmetric matrices are needed in the treatment of generalized eigenvalue problems with Hamiltonian structure that arise, e.g., in the analysis of corner singularities in elasticity and in linear quadratic optimal control problems. These applications are also discussed in the paper.
reviewed by: Ulrich Langer
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 1533611
zbMATH Keywords: matrix factorizations
zbMATH Keywords: Hamiltonian eigenproblems
zbMATH Keywords: complete pivoting
zbMATH Keywords: skew-symmetric matrices
zbMATH Keywords: corner singularities
zbMATH Keywords: elasticity
zbMATH Keywords: linear quadratic optimal control problems
MaRDI profile type: Publication
published in: ETNA - Electronic Transactions on Numerical Analysis
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description: scientific article; zbMATH DE number 1533611