Block Gram-Schmidt algorithms and their stability properties
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00550984" target="_blank" >RIV/67985840:_____/22:00550984 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/22:10452869
Result on the web
<a href="https://doi.org/10.1016/j.laa.2021.12.017" target="_blank" >https://doi.org/10.1016/j.laa.2021.12.017</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.laa.2021.12.017" target="_blank" >10.1016/j.laa.2021.12.017</a>
Alternative languages
Result language
angličtina
Original language name
Block Gram-Schmidt algorithms and their stability properties
Original language description
Block Gram-Schmidt algorithms serve as essential kernels in many scientific computing applications, but for many commonly used variants, a rigorous treatment of their stability properties remains open. This work provides a comprehensive categorization of block Gram-Schmidt algorithms, particularly those used in Krylov subspace methods to build orthonormal bases one block vector at a time. Known stability results are assembled, and new results are summarized or conjectured for important communication-reducing variants. Additionally, new block versions of low-synchronization variants are derived, and their efficacy and stability are demonstrated for a wide range of challenging examples. Numerical examples are computed with a versatile Matlab package hosted at https://github.com/katlund/BlockStab, and scripts for reproducing all results in the paper are provided. Block Gram-Schmidt implementations in popular software packages are discussed, along with a number of open problems. An appendix containing all algorithms type-set in a uniform fashion is provided.
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
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA20-01074S" target="_blank" >GA20-01074S: Adaptive methods for the numerical solution of partial differential equations: analysis, error estimates and iterative solvers</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Linear Algebra and Its Applications
ISSN
0024-3795
e-ISSN
1873-1856
Volume of the periodical
638
Issue of the periodical within the volume
April 1
Country of publishing house
US - UNITED STATES
Number of pages
46
Pages from-to
150-195
UT code for WoS article
000777811000006
EID of the result in the Scopus database
2-s2.0-85122191862