Mixed Precision Iterative Refinement for Least Squares With Linear Equality Constraints and Generalized Least Squares Problems
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10511864" target="_blank" >RIV/00216208:11320/25:10511864 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=kwM_f5Sjnf" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=kwM_f5Sjnf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/nla.70036" target="_blank" >10.1002/nla.70036</a>
Alternative languages
Result language
angličtina
Original language name
Mixed Precision Iterative Refinement for Least Squares With Linear Equality Constraints and Generalized Least Squares Problems
Original language description
Recent development on mixed precision techniques has largely enhanced the performance of various linear algebra solvers, one of which is the solver for the least squares problem. By transforming least squares problems into augmented linear systems, mixed precision techniques are capable of refining the lower precision solution to the working precision. In this paper, we propose mixed precision iterative refinement algorithms for two variants of the least squares problems-the least squares problem with linear equality constraints (LSE) and the generalized least squares problem (GLS). Both classical and GMRES-based iterative refinement can be applied to augmented systems of these two problems to improve the accuracy of the solution. For reasonably well-conditioned problems, our algorithms reduce the execution time by a factor of 40% on average compared to the fixed precision ones from LAPACK on the x86-64 architecture.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
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Continuities
R - Projekt Ramcoveho programu EK
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Numerical Linear Algebra with Applications
ISSN
1070-5325
e-ISSN
1099-1506
Volume of the periodical
32
Issue of the periodical within the volume
5
Country of publishing house
GB - UNITED KINGDOM
Number of pages
21
Pages from-to
e70036
UT code for WoS article
001605978500007
EID of the result in the Scopus database
2-s2.0-105015405537