Block Gram-Schmidt algorithms and their stability properties

Kód výsledku v IS VaVaI

RIV/67985840:_____/22:00550984 - isvavai.cz

Nalezeny alternativní kódy

RIV/00216208:11320/22:10452869

Výsledek na webu

https://doi.org/10.1016/j.laa.2021.12.017

DOI - Digital Object Identifier

10.1016/j.laa.2021.12.017

Jazyk výsledku

angličtina

Název v původním jazyce

Block Gram-Schmidt algorithms and their stability properties

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Block Gram-Schmidt algorithms and their stability properties

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

GA20-01074S: Adaptivní metody pro numerické řešení parciálních diferenciálních rovnic: analýza, odhady chyb a iterativní řešiče

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Linear Algebra and Its Applications

ISSN

0024-3795

e-ISSN

1873-1856

Svazek periodika

638

Číslo periodika v rámci svazku

April 1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

46

Strana od-do

150-195

Kód UT WoS článku

000777811000006

EID výsledku v databázi Scopus

2-s2.0-85122191862