ePubs
The open archive for STFC research publications
Home
About ePubs
Content Policies
News
Help
Privacy/Cookies
Suggest an Enhancement
Contact ePubs
Full Record Details
Persistent URL
http://purl.org/net/epubs/work/53474
Record Status
Checked
Record Id
53474
Title
Generalized Golub-Kahan bidiagonalization and stopping criteria
Contributors
M Arioli (STFC Rutherford Appleton Lab.)
Abstract
The Golub-Kahan bidiagonalization algorithm has been widely used in solving least-squares problems and in the computation of the SVD of rectangular matrices. Here we propose an algo- rithm based on the Golub-Kahan process for the solution of augmented systems that minimizes the norm of the error and, in particular, we propose a novel estimator of the error similar to the one proposed by Hestenes-Stiefel for the conjugate gradient. This estimator gives a lower bound for the error, and can be used as a reliable stopping criterion for the whole process. We also pro- pose an upper bound of the error base on Gauss-Radau quadrature. Finally, we show how we can transform and optimally precondition augmented systems rising from the mixed finite-element approximation of differential problems.
Organisation
CSE-NAG
,
STFC
,
SCI-COMP
Keywords
Bidiagonalization
,
stopping criteria
,
Engineering
Funding Information
Related Research Object(s):
Licence Information:
Language
English (EN)
Type
Details
URI(s)
Local file(s)
Year
Journal Article
SIAM J Matrix Anal A
34, no. 2 (2013): 86654, 593-623.
doi:10.1137/120866543
86654.pdf
2013
Showing record 1 of 1
Recent Additions
Browse Organisations
Browse Journals/Series
Login to add & manage publications and access information for OA publishing
Username:
Password:
Useful Links
Chadwick & RAL Libraries
SHERPA FACT
SHERPA RoMEO
SHERPA JULIET
Journal Checker Tool
Google Scholar