Accurate error estimation in CG

Result code in 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>

Alternative codes found

RIV/00216208:11320/21:10436065

Result on the web

<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>

Result language

angličtina

Original language name

Accurate error estimation in CG

Original language description

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.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

<a href="/en/project/GA20-01074S" target="_blank" >GA20-01074S: Adaptive methods for the numerical solution of partial differential equations: analysis, error estimates and iterative solvers</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2021

Confidentiality

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

Name of the periodical

Numerical Algorithms

ISSN

1017-1398

e-ISSN

1572-9265

Volume of the periodical

88

Issue of the periodical within the volume

3

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

23

Pages from-to

1337-1359

UT code for WoS article

000635870100002

EID of the result in the Scopus database

2-s2.0-85103422252