Avoiding Breakdown in Incomplete Factorizations in Low Precision Arithmetic
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10490638" target="_blank" >RIV/00216208:11320/24:10490638 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Jb-26~xlP_" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Jb-26~xlP_</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1145/3651155" target="_blank" >10.1145/3651155</a>
Alternative languages
Result language
angličtina
Original language name
Avoiding Breakdown in Incomplete Factorizations in Low Precision Arithmetic
Original language description
The emergence of low precision floating-point arithmetic in computer hardware has led to a resurgence of interest in the use of mixed precision numerical linear algebra. For linear systems of equations, there has been renewed enthusiasm for mixed precision variants of iterative refinement. We consider the iterative solution of large sparse systems using incomplete factorization preconditioners. The focus is on the robust computation of such preconditioners in half precision arithmetic and employing them to solve symmetric positive definite systems to higher precision accuracy; however, the proposed ideas can be applied more generally. Even for well-conditioned problems, incomplete factorizations can break down when small entries occur on the diagonal during the factorization. When using half precision arithmetic, overflows are an additional possible source of breakdown. We examine how breakdowns can be avoided and implement our strategies within new half precision Fortran sparse incomplete Cholesky factorization software. Results are reported for a range of problems from practical applications. These demonstrate that, even for highly ill-conditioned problems, half precision preconditioners can potentially replace double precision preconditioners, although unsurprisingly this may be at the cost of additional iterations of a Krylov solver.
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
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
ACM Transactions on Mathematical Software
ISSN
0098-3500
e-ISSN
1557-7295
Volume of the periodical
50
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
25
Pages from-to
9
UT code for WoS article
001266982400001
EID of the result in the Scopus database
2-s2.0-85194009969