A Newton-based method for the calculation of the distance to instability
type: Item
instance of: scholarly article
title: A Newton-based method for the calculation of the distance to instability
zbMATH Open document ID: 1228.65065
published in: Linear Algebra and its Applications
publication date: 2011-09-22T00:00:00Z
review text: The authors introduce a new fast algorithm for computing the distance of a stable matrix, with all its eigenvalues in the left half-plane, to the set of unstable matrices. The first component of the algorithm is a local method based on Newtons's method, and though very quick, is not guaranteed to find a globally optimal solution. For that reason, a checking step is added to provide a global method. Numerical results show that this algorithm is competitive with and, in almost all cases, outperforms earlier algorithms. Five numerical examples are considered.
reviewed by: Rémi Vaillancourt
Mathematics Subject Classification ID: 65F30
zbMATH DE Number: 5949271
zbMATH Keywords: stable matrices
zbMATH Keywords: distance to instability
zbMATH Keywords: fast algorithm
zbMATH Keywords: Newtons's method
zbMATH Keywords: numerical results
author: Melina A. Freitag
author: Alastair Spence
describes a project that uses: MatrixMarket
MaRDI profile type: Publication
full work available at URL: j.laa.2011.06.012
OpenAlex ID: W2087462091
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DOI: 10.1016/J.LAA.2011.06.012
description: scientific article; zbMATH DE number 5949271