Self-equivalent flows associated with the generalized eigenvalue problem
type: Item
instance of: scholarly article
title: Self-equivalent flows associated with the generalized eigenvalue problem
zbMATH Open document ID: 0684.65037
DOI: 10.1016/0024-3795(89)90576-4
published in: Linear Algebra and its Applications
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://pub.uni-bielefeld.de/record/1780573
review text: The authors use elementary Lie theory to develop a family of algorithms for solving the generalized eigenvalue problem \(Ax=\lambda Bx\) for arbitrary pairs of nonsingular matrices. The family (referred as FGZ algorithms) includes the well known LZ algorithm of \textit{L. Kaufman} [SIAM J. Numer. Anal. 11, 997-1024 (1974; Zbl 0294.65025)] and the QZ algorithm of \textit{C. B. Moler} and \textit{G. W. Stewart} [SIAM J. Numer. Anal. 10, 241-256 (1973; Zbl 0225.65046)], as well as new algorithms called SZ and HZ. The continuous analogues of the unshifted and shifted LZ and QZ algorithms are presented. For each considered algorithm a family of associated flows is constructed.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 37C10
zbMATH DE Number: 4121302
zbMATH Keywords: self-equivalent flows
zbMATH Keywords: Lie theory
zbMATH Keywords: generalized eigenvalue problem
zbMATH Keywords: FGZ algorithms
zbMATH Keywords: LZ algorithm
zbMATH Keywords: QZ algorithm
author: David S. Watkins
author: Ludwig Elsner
MaRDI profile type: Publication
OpenAlex ID: W2036833905
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description: scientific article; zbMATH DE number 4121302