Verified bounds for singular values, in particular for the spectral norm of a matrix and its inverse

Publikationstyp
Journal Article
Date Issued
2010-11-11
Sprache
English
Author(s)
Rump, Siegfried M.  orcid-logo
Institut
Zuverlässiges Rechnen E-19  
TORE-URI
http://hdl.handle.net/11420/7925
Journal
BIT  
Volume
51
Issue
2
Start Page
367
End Page
384
Citation
BIT Numerical Mathematics 2 (51): 367-384 (2011-06-01)
Publisher DOI
10.1007/s10543-010-0294-0
Scopus ID
2-s2.0-79958241524
Publisher
Springer Science Business Media B.V.
The singular value decomposition and spectral norm of a matrix are ubiquitous in numerical analysis. They are extensively used in proofs, but usually it is not necessary to compute them. However, there are some important applications in the realm of verified error bounds for the solution of ordinary and partial differential equations where reasonably tight error bounds for the spectral norm of a matrix are mandatory. We present various approaches to this together with some auxiliary useful estimates. © 2010 Springer Science + Business Media B.V.
Subjects
Condition number
Error bounds
INTLAB
Spectral norm
Verification
DDC Class
004: Informatik
510: Mathematik