Exponential splittings of products of matrices and accurately computing singular values of long products
type: Item
instance of: scholarly article
title: Exponential splittings of products of matrices and accurately computing singular values of long products
zbMATH Open document ID: 0955.65028
DOI: 10.1016/S0024-3795(99)00273-6
author: Suely Oliveira
author: David E. Stewart
published in: Linear Algebra and its Applications
publication date: 2001-02-14T00:00:00Z
review text: The authors discuss the influence of perturbations \(E_i\) in the factors of long products \(A_n \cdots A_1\) of matrices on the relative error of the singular values of such products. This relative errors can be quite large in general. But as it is shown in the paper, the error in the singular values is \({\mathcal O}(n^2 \max_i \kappa_2(A_i) \|E_i\|_F)\) if the product has an exponential splitting. Numerical examples illustrating the behaviour of the relative errors in the singular values are presented.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 37M25
zbMATH DE Number: 1443449
zbMATH Keywords: products of matrices
zbMATH Keywords: singular values
zbMATH Keywords: exponential splitting
zbMATH Keywords: stability
zbMATH Keywords: Lyapunov exponents
zbMATH Keywords: numerical examples
reviewed by: Michael Jung
describes a project that uses: mctoolbox
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1443449