MIXED PRECISION SKETCHING FOR LEAST-SQUARES PROBLEMS AND ITS APPLICATION IN GMRES-BASED ITERATIVE REFINEMENT
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10509866" target="_blank" >RIV/00216208:11320/25:10509866 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=p8L8llcBcT" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=p8L8llcBcT</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/24M1702246" target="_blank" >10.1137/24M1702246</a>
Alternative languages
Result language
angličtina
Original language name
MIXED PRECISION SKETCHING FOR LEAST-SQUARES PROBLEMS AND ITS APPLICATION IN GMRES-BASED ITERATIVE REFINEMENT
Original language description
Sketching-based preconditioners have been shown to accelerate the solution of dense least-squares problems with coefficient matrices having substantially more rows than columns. The cost of generating these preconditioners can be reduced by employing low precision floating-point formats for all or part of the computations. We perform finite precision analysis of a mixed precision algorithm that computes the R-factor of a QR factorization of the sketched coefficient matrix. Two precisions can be chosen and the analysis allows understanding how to set these precisions to exploit the potential benefits of low precision formats and still guarantee an effective preconditioner. If the nature of the least-squares problem requires a solution with a small forward error, then mixed precision iterative refinement (IR) may be needed. For ill-conditioned problems the GMRES-based IR approach can be used, but good preconditioner is crucial to ensure convergence. We theoretically show when the sketching-based preconditioner can guarantee that the GMRES-based IR reduces the relative forward error of the least-squares solution and the residual to the level of the working precision unit roundoff. Small numerical examples illustrate the analysis.
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
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
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
SIAM Journal on Matrix Analysis and Applications
ISSN
0895-4798
e-ISSN
1095-7162
Volume of the periodical
46
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
20
Pages from-to
2041-2060
UT code for WoS article
001580457700005
EID of the result in the Scopus database
2-s2.0-105015737412