SOLVING MIXED SPARSE-DENSE LINEAR LEAST-SQUARES PROBLEMS BY PRECONDITIONED ITERATIVE METHODS

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10369987" target="_blank" >RIV/00216208:11320/17:10369987 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1137/16M1108339" target="_blank" >http://dx.doi.org/10.1137/16M1108339</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/16M1108339" target="_blank" >10.1137/16M1108339</a>

Jazyk výsledku

angličtina

Název v původním jazyce

SOLVING MIXED SPARSE-DENSE LINEAR LEAST-SQUARES PROBLEMS BY PRECONDITIONED ITERATIVE METHODS

Popis výsledku v původním jazyce

The efficient solution of large linear least-squares problems in which the system matrix A contains rows with very different densities is challenging. Previous work has focused on direct methods for problems in which A has a few relatively dense rows. These rows are initially ignored, a factorization of the sparse part is computed using a sparse direct solver, and then the solution is updated to take account of the omitted dense rows. In some practical applications the number of dense rows can be significant, and for very large problems, using a direct solver may not be feasible. We propose processing rows that are identified as dense separately within a conjugate gradient method using an incomplete factorization preconditioner combined with the factorization of a dense matrix of size equal to the number of dense rows. Numerical experiments on large-scale problems from real applications are used to illustrate the effectiveness of our approach. The results demonstrate that we can efficiently solve problems that could not be solved by a preconditioned conjugate gradient method without exploiting the dense rows.

Název v anglickém jazyce

SOLVING MIXED SPARSE-DENSE LINEAR LEAST-SQUARES PROBLEMS BY PRECONDITIONED ITERATIVE METHODS

Popis výsledku anglicky

The efficient solution of large linear least-squares problems in which the system matrix A contains rows with very different densities is challenging. Previous work has focused on direct methods for problems in which A has a few relatively dense rows. These rows are initially ignored, a factorization of the sparse part is computed using a sparse direct solver, and then the solution is updated to take account of the omitted dense rows. In some practical applications the number of dense rows can be significant, and for very large problems, using a direct solver may not be feasible. We propose processing rows that are identified as dense separately within a conjugate gradient method using an incomplete factorization preconditioner combined with the factorization of a dense matrix of size equal to the number of dense rows. Numerical experiments on large-scale problems from real applications are used to illustrate the effectiveness of our approach. The results demonstrate that we can efficiently solve problems that could not be solved by a preconditioned conjugate gradient method without exploiting the dense rows.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GC17-04150J" target="_blank" >GC17-04150J: Robustní dvojúrovňové simulace založené na Fourierově metodě a metodě konečných prvků: Odhady chyb, redukované modely a stochastika</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

SIAM Journal of Scientific Computing

ISSN

1064-8275

e-ISSN

—

Svazek periodika

39

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

16

Strana od-do

"A2422"-"A2437"

Kód UT WoS článku

000418659900013

EID výsledku v databázi Scopus

2-s2.0-85039997560