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On Kogbetliantz's SVD algorithm in the presence of clusters

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Charlier , J.P. [Philips Research Lab Brussels] Van Dooren, Paul [UCL]

We consider matrices with off-diagonal blocks of small norm and derive tight bounds for the approximation of their singular values by those of their diagonal blocks. These results are used to show that triangular matrices with clusters of singular values must possess a principal submatrix of “nearly” diagonal form. From the latter we then derive results pertaining to the quadratic convergence of Kogbetliantz’s algorithm for computing the SVD, in the presence of clusters.

Document type Article de périodique (Journal article)
Publication date 1987
Language Anglais
Journal information "Linear Algebra and Its Applications" - Vol. 95, p. 135-160 (1987)
Peer reviewed yes
Publisher Elsevier Inc. ((United States) New York)
issn 0024-3795
Publication status Publié
Affiliations Philips Research Lab Brussels - Applied Mathematics
UCL - FSA/INMA - Département d'ingénierie mathématique
Links
Bibliographic reference Charlier , J.P. ; Van Dooren, Paul. On Kogbetliantz's SVD algorithm in the presence of clusters. In: Linear Algebra and Its Applications, Vol. 95, p. 135-160 (1987)
Permanent URL http://hdl.handle.net/2078.1/80963