An adaptive s-step conjugate gradient algorithm with dynamic basis updating

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10420369" target="_blank" >RIV/00216208:11320/20:10420369 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=QL3~wBCdgg" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=QL3~wBCdgg</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.21136/AM.2020.0136-19" target="_blank" >10.21136/AM.2020.0136-19</a>

Jazyk výsledku

angličtina

Název v původním jazyce

An adaptive s-step conjugate gradient algorithm with dynamic basis updating

Popis výsledku v původním jazyce

The adaptive s-step CG algorithm is a solver for sparse symmetric positive definite linear systems designed to reduce the synchronization cost per iteration while still achieving a user-specified accuracy requirement. In this work, we improve the adaptive s-step conjugate gradient algorithm by the use of iteratively updated estimates of the largest and smallest Ritz values, which give approximations of the largest and smallest eigenvalues of A, using a technique due to G.Meurant and P.Tichy (2018). The Ritz value estimates are used to dynamically update parameters for constructing Newton or Chebyshev polynomials so that the conditioning of the s-step bases can be continuously improved throughout the iterations. These estimates are also used to automatically set a variable related to the ratio of the sizes of the error and residual, which was previously treated as an input parameter. We show through numerical experiments that in many cases the new algorithm improves upon the previous adaptive s-step approach both in terms of numerical behavior and reduction in number of synchronizations.

Název v anglickém jazyce

An adaptive s-step conjugate gradient algorithm with dynamic basis updating

Popis výsledku anglicky

The adaptive s-step CG algorithm is a solver for sparse symmetric positive definite linear systems designed to reduce the synchronization cost per iteration while still achieving a user-specified accuracy requirement. In this work, we improve the adaptive s-step conjugate gradient algorithm by the use of iteratively updated estimates of the largest and smallest Ritz values, which give approximations of the largest and smallest eigenvalues of A, using a technique due to G.Meurant and P.Tichy (2018). The Ritz value estimates are used to dynamically update parameters for constructing Newton or Chebyshev polynomials so that the conditioning of the s-step bases can be continuously improved throughout the iterations. These estimates are also used to automatically set a variable related to the ratio of the sizes of the error and residual, which was previously treated as an input parameter. We show through numerical experiments that in many cases the new algorithm improves upon the previous adaptive s-step approach both in terms of numerical behavior and reduction in number of synchronizations.

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

2020

Kód důvěrnosti údajů

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

Název periodika

Applications of Mathematics

ISSN

0862-7940

e-ISSN

—

Svazek periodika

65

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

29

Strana od-do

123-151

Kód UT WoS článku

000525004700002

EID výsledku v databázi Scopus

2-s2.0-85083324122