An adaptive s-step conjugate gradient algorithm with dynamic basis updating
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
An adaptive s-step conjugate gradient algorithm with dynamic basis updating
Original language description
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.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Applications of Mathematics
ISSN
0862-7940
e-ISSN
—
Volume of the periodical
65
Issue of the periodical within the volume
2
Country of publishing house
CZ - CZECH REPUBLIC
Number of pages
29
Pages from-to
123-151
UT code for WoS article
000525004700002
EID of the result in the Scopus database
2-s2.0-85083324122