Mixed Precision Iterative Refinement for Least Squares With Linear Equality Constraints and Generalized Least Squares Problems
Identifikátory výsledku
Kód výsledku v 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>
Výsledek na webu
<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>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Mixed Precision Iterative Refinement for Least Squares With Linear Equality Constraints and Generalized Least Squares Problems
Popis výsledku v původním jazyce
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.
Název v anglickém jazyce
Mixed Precision Iterative Refinement for Least Squares With Linear Equality Constraints and Generalized Least Squares Problems
Popis výsledku anglicky
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.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10102 - Applied mathematics
Návaznosti výsledku
Projekt
—
Návaznosti
R - Projekt Ramcoveho programu EK
Ostatní
Rok uplatnění
2025
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Numerical Linear Algebra with Applications
ISSN
1070-5325
e-ISSN
1099-1506
Svazek periodika
32
Číslo periodika v rámci svazku
5
Stát vydavatele periodika
GB - Spojené království Velké Británie a Severního Irska
Počet stran výsledku
21
Strana od-do
e70036
Kód UT WoS článku
001605978500007
EID výsledku v databázi Scopus
2-s2.0-105015405537