The DQR algorithm, basic theory, convergence, and conditional stability
type: Item
instance of: scholarly article
title: The DQR algorithm, basic theory, convergence, and conditional stability
zbMATH Open document ID: 0883.65029
published in: Numerische Mathematik
publication date: 1997-07-23T00:00:00Z
review text: The work is dedicated to the general eigenvalue problem and discusses the DQR method as an alternative to the standard QR algorithm. The given dense matrix is reduced to general tridiagonal form (instead of Hessenberg form). For the iterative part D-orthogonal similarity transformations are used, which preserve the tridiagonal structure and thus allow computation of all eigenvalues with \(O(n^2)\) flop. Since the DQR method can be unstable the author proposes a hybrid algorithm, which switches to standard QR if application of DQR fails. The article contains theoretical investigations of convergence and stability behavior of the DQR method as well as exhaustive discussions of numerical examples.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 1037313
zbMATH Keywords: unsymmetric eigenvalue problem
zbMATH Keywords: orthogonal reduction
zbMATH Keywords: QR algorithm
zbMATH Keywords: convergence
zbMATH Keywords: stability
zbMATH Keywords: numerical examples
author: Frank Uhlig
reviewed by: Andreas Frommer
MaRDI profile type: Publication
full work available at URL: s002110050275
OpenAlex ID: W264482033
DOI: 10.1007/S002110050275
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description: scientific article; zbMATH DE number 1037313