A Note on Adaptivity in Factorized Approximate Inverse Preconditioning

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F20%3A00525243" target="_blank" >RIV/67985807:_____/20:00525243 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/46747885:24220/20:00007782

Výsledek na webu

<a href="https://www.anstuocmath.ro/volume-xxviii-2020-fascicola-2.html" target="_blank" >https://www.anstuocmath.ro/volume-xxviii-2020-fascicola-2.html</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.2478/auom-2020-0024" target="_blank" >10.2478/auom-2020-0024</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A Note on Adaptivity in Factorized Approximate Inverse Preconditioning

Popis výsledku v původním jazyce

The problem of solving large-scale systems of linear algebraic equations arises in a wide range of applications. In many cases the preconditioned iterative method is a method of choice. This paper deals with the approximate inverse preconditioning AINV/SAINV based on the incomplete generalized Gram-Schmidt process. This type of the approximate inverse preconditioning has been repeatedly used for matrix diagonalization in computation of electronic structures but approximating inverses is of an interest in parallel computations in general. Our approach uses adaptive dropping of the matrix entries with the control based on the computed intermediate quantities. Strategy has been introduced as a way to solve difficult application problems and it is motivated by recent theoretical results on the loss of orthogonality in the generalized Gram-Schmidt process. Nevertheless, there are more aspects of the approach that need to be better understood. The diagonal pivoting based on a rough estimation of condition numbers of leading principal submatrices can sometimes provide inefficient preconditioners. This short study proposes another type of pivoting, namely the pivoting that exploits incremental condition estimation based on monitoring both direct and inverse factors of the approximate factorization. Such pivoting remains rather cheap and it can provide in many cases more reliable preconditioner. Numerical examples from real-world problems, small enough to enable a full analysis, are used to illustrate the potential gains of the new approach.

Název v anglickém jazyce

A Note on Adaptivity in Factorized Approximate Inverse Preconditioning

Popis výsledku anglicky

The problem of solving large-scale systems of linear algebraic equations arises in a wide range of applications. In many cases the preconditioned iterative method is a method of choice. This paper deals with the approximate inverse preconditioning AINV/SAINV based on the incomplete generalized Gram-Schmidt process. This type of the approximate inverse preconditioning has been repeatedly used for matrix diagonalization in computation of electronic structures but approximating inverses is of an interest in parallel computations in general. Our approach uses adaptive dropping of the matrix entries with the control based on the computed intermediate quantities. Strategy has been introduced as a way to solve difficult application problems and it is motivated by recent theoretical results on the loss of orthogonality in the generalized Gram-Schmidt process. Nevertheless, there are more aspects of the approach that need to be better understood. The diagonal pivoting based on a rough estimation of condition numbers of leading principal submatrices can sometimes provide inefficient preconditioners. This short study proposes another type of pivoting, namely the pivoting that exploits incremental condition estimation based on monitoring both direct and inverse factors of the approximate factorization. Such pivoting remains rather cheap and it can provide in many cases more reliable preconditioner. Numerical examples from real-world problems, small enough to enable a full analysis, are used to illustrate the potential gains of the new approach.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA17-12925S" target="_blank" >GA17-12925S: Pevnost materiálů a strojních součástí na bázi železa: Víceškálový přístup</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

Analele Stiintifice ale Universitatii Ovidius Constanta-Seria Matematica

ISSN

1224-1784

e-ISSN

—

Svazek periodika

28

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

RO - Rumunsko

Počet stran výsledku

11

Strana od-do

149-159

Kód UT WoS článku

000574556300009

EID výsledku v databázi Scopus

2-s2.0-85093503628