ERROR NORM ESTIMATES FOR THE BLOCK CONJUGATE GRADIENT ALGORITHMS
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10509000" target="_blank" >RIV/00216208:11320/25:10509000 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=j-MeGFN6HZ" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=j-MeGFN6HZ</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/25M1735408" target="_blank" >10.1137/25M1735408</a>
Alternative languages
Result language
angličtina
Original language name
ERROR NORM ESTIMATES FOR THE BLOCK CONJUGATE GRADIENT ALGORITHMS
Original language description
In the book [G. Meurant and P. Tichy, Error Norm Estimation in the Conjugate Gradient Algorithm, SIAM, 2024], we discussed the estimation of error norms in the conjugate gradient (CG) algorithm for solving linear systems Ax = b with a symmetric positive definite matrix A, where b and x are vectors. In this paper, we generalize the most important formulas for estimating the A-norm of the error to the block case. First, we discuss in detail the derivation of various variants of the block CG (BCG) algorithm from the block Lanczos algorithm. We then consider BCG and derive the related block Gauss and block Gauss--Radau quadrature rules. We show how to obtain lower and upper bounds on the A-norm of the error of each system, both in terms of the quantities computed in BCG and in terms of the underlying block Lanczos algorithm. Numerical experiments demonstrate the behavior of the bounds in practical computations.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SIAM Journal on Matrix Analysis and Applications
ISSN
0895-4798
e-ISSN
1095-7162
Volume of the periodical
46
Issue of the periodical within the volume
4
Country of publishing house
US - UNITED STATES
Number of pages
22
Pages from-to
2175-2196
UT code for WoS article
001606914200001
EID of the result in the Scopus database
2-s2.0-105019397722