Result: On the Convergence of Stewart's QLP Algorithm for Approximating the SVD: On the convergence of Stewart's QLP algorithm for approximating the SVD

Title:
On the Convergence of Stewart's QLP Algorithm for Approximating the SVD: On the convergence of Stewart's QLP algorithm for approximating the SVD
Authors:
Huckaby, David A., Chan, Tony F.
Source:
Numerical Algorithms. 32:287-316
Publisher Information:
Springer Science and Business Media LLC, 2003.
Publication Year:
2003
Subject Terms:
Numerical computation of eigenvalues and eigenvectors of matrices, numerical examples, Numerical solutions to overdetermined systems, pseudoinverses, algorithm, convergence, QLP, 01 natural sciences, QR, Pivoted QLP decomposition, Singular values, pivoted QLP decomposition, singular value decomposition (SVD), 0101 mathematics, SVD
Document Type:
Academic journal Article
File Description:
application/xml
Language:
English
ISSN:
1572-9265
1017-1398
DOI:
10.1023/a:1024082314087
Access URL:
https://zbmath.org/1960076
https://doi.org/10.1023/a:1024082314087
https://ui.adsabs.harvard.edu/abs/2003NuAlg..32..287H/abstract
http://repository.ust.hk/ir/Record/1783.1-52271
https://link.springer.com/content/pdf/10.1023/A:1024082314087.pdf
https://link.springer.com/article/10.1023%2FA%3A1024082314087
Rights:
Springer Nature TDM
Accession Number:
edsair.doi.dedup.....ef0ecded78f5cc18a15c28ac4a84b6eb
Database:
OpenAIRE

Further Information

This paper tries to explain some of the success of Stewart's QLP algorithm [cf.\textit{G. W. Stewart}, SIAM J. Sci. Comput. 20, 1336--1348 (1999; Zbl 0939.65062)] in computing the singular values of a matrix. It discusses the tracking of singular values throughout the computation, and studies the convergence of the QLP. To be applicable, the theory developed requires a gap in the singular values, which does not yet explain everything. The paper closes with considering the asymptotic rate of convergence as well as some numerical examples.