On Kogbetliantz's SVD algorithm in the presence of clusters
(1987) Linear Algebra and Its Applications — Vol. 95, p. 135-160 (1987)
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- Abstract
- 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.
- Affiliations
Philips Research Lab Brussels Applied Mathematics
Citations
Charlier, J. P., & Van Dooren, P. (1987). On Kogbetliantz’s SVD algorithm in the presence of clusters. Linear Algebra and Its Applications, 95, 135-160. https://hdl.handle.net/2078.5/70904 (Original work published 1987)