Block CG algorithms revisited
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10501905" target="_blank" >RIV/00216208:11320/25:10501905 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=V9Tks4d17x" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=V9Tks4d17x</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11075-025-02038-4" target="_blank" >10.1007/s11075-025-02038-4</a>
Alternative languages
Result language
angličtina
Original language name
Block CG algorithms revisited
Original language description
Our goal in this paper is to clarify the relationship between the block Lanczos and the block conjugate gradient (BCG) algorithms. Under the full rank assumption for the block vectors, we show the one-to-one correspondence between the algorithms. This allows, for example, the computation of the block Lanczos coefficients in BCG. The availability of block Jacobi matrices in BCG opens the door for further development, e.g., for error estimation in BCG based on (modified) block Gauss quadrature rules. Driven by the need to get a practical variant of the BCG algorithm well suited for computations in finite precision arithmetic, we also discuss some important variants of BCG due to Dubrulle. These variants avoid the troubles with a possible rank deficiency within the block vectors. We show how to incorporate preconditioning and computation of Lanczos coefficients into these variants. We hope to help clarify which variant of the block conjugate gradient algorithm should be used for computations in finite precision arithmetic. Numerical results illustrate the performance of different variants of BCG on some examples.
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
Numerical Algorithms
ISSN
1017-1398
e-ISSN
1572-9265
Volume of the periodical
100
Issue of the periodical within the volume
March 2025
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
27
Pages from-to
1527-1553
UT code for WoS article
001438958500001
EID of the result in the Scopus database
2-s2.0-86000290015