MIXED PRECISION ITERATIVE REFINEMENT WITH SPARSE APPROXIMATE INVERSE PRECONDITIONING
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10475691" target="_blank" >RIV/00216208:11320/23:10475691 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=.t88-EHo7z" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=.t88-EHo7z</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/22M1487709" target="_blank" >10.1137/22M1487709</a>
Alternative languages
Result language
angličtina
Original language name
MIXED PRECISION ITERATIVE REFINEMENT WITH SPARSE APPROXIMATE INVERSE PRECONDITIONING
Original language description
With the commercial availability of mixed precision hardware, mixed precision GMRES-based iterative refinement schemes have emerged as popular approaches for solving sparse linear systems. Existing analyses of these approaches, however, are based on using full LU factorizations to construct preconditioners for use within GMRES in each refinement step. In practical applications, inexact preconditioning techniques, such as incomplete LU or sparse approximate inverses, are often used for performance reasons. In this work, we investigate the use of sparse approximate inverse preconditioners based on Frobenius norm minimization within GMRES-based iterative refinement. We analyze the computation of sparse approximate inverses in finite precision and derive constraints under which user-specified stopping criteria will be satisfied. We then analyze the behavior of and convergence constraints for a five-precision GMRES-based iterative refinement scheme that uses sparse approximate inverse preconditioning, which we call SPAI-GMRES-IR. Our numerical experiments confirm the theoretical analysis and illustrate the resulting tradeoffs between preconditioner sparsity and GMRES-IR convergence rate.
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
2023
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 of Scientific Computing
ISSN
1064-8275
e-ISSN
1095-7197
Volume of the periodical
45
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
23
Pages from-to
"C131"-"C153"
UT code for WoS article
001071048600020
EID of the result in the Scopus database
2-s2.0-85163176309