Accurate error estimation in CG

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00546795" target="_blank" >RIV/67985840:_____/21:00546795 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216208:11320/21:10436065

Výsledek na webu

<a href="https://doi.org/10.1007/s11075-021-01078-w" target="_blank" >https://doi.org/10.1007/s11075-021-01078-w</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11075-021-01078-w" target="_blank" >10.1007/s11075-021-01078-w</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Accurate error estimation in CG

Popis výsledku v původním jazyce

In practical computations, the (preconditioned) conjugate gradient (P)CG method is the iterative method of choice for solving systems of linear algebraic equations Ax = b with a real symmetric positive definite matrix A. During the iterations, it is important to monitor the quality of the approximate solution xk so that the process could be stopped whenever xk is accurate enough. One of the most relevant quantities for monitoring the quality of xk is the squared A-norm of the error vector x − xk. This quantity cannot be easily evaluated, however, it can be estimated. Many of the existing estimation techniques are inspired by the view of CG as a procedure for approximating a certain Riemann–Stieltjes integral. The most natural technique is based on the Gauss quadrature approximation and provides a lower bound on the quantity of interest. The bound can be cheaply evaluated using terms that have to be computed anyway in the forthcoming CG iterations.

Název v anglickém jazyce

Accurate error estimation in CG

Popis výsledku anglicky

In practical computations, the (preconditioned) conjugate gradient (P)CG method is the iterative method of choice for solving systems of linear algebraic equations Ax = b with a real symmetric positive definite matrix A. During the iterations, it is important to monitor the quality of the approximate solution xk so that the process could be stopped whenever xk is accurate enough. One of the most relevant quantities for monitoring the quality of xk is the squared A-norm of the error vector x − xk. This quantity cannot be easily evaluated, however, it can be estimated. Many of the existing estimation techniques are inspired by the view of CG as a procedure for approximating a certain Riemann–Stieltjes integral. The most natural technique is based on the Gauss quadrature approximation and provides a lower bound on the quantity of interest. The bound can be cheaply evaluated using terms that have to be computed anyway in the forthcoming CG iterations.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA20-01074S" target="_blank" >GA20-01074S: Adaptivní metody pro numerické řešení parciálních diferenciálních rovnic: analýza, odhady chyb a iterativní řešiče</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Numerical Algorithms

ISSN

1017-1398

e-ISSN

1572-9265

Svazek periodika

88

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

23

Strana od-do

1337-1359

Kód UT WoS článku

000635870100002

EID výsledku v databázi Scopus

2-s2.0-85103422252