Avoiding Breakdown in Incomplete Factorizations in Low Precision Arithmetic

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Avoiding Breakdown in Incomplete Factorizations in Low Precision Arithmetic

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Avoiding Breakdown in Incomplete Factorizations in Low Precision Arithmetic

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

ACM Transactions on Mathematical Software

ISSN

0098-3500

e-ISSN

1557-7295

Svazek periodika

50

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

25

Strana od-do

9

Kód UT WoS článku

001266982400001

EID výsledku v databázi Scopus

2-s2.0-85194009969