On finite precision block Lanczos computations
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10509004" target="_blank" >RIV/00216208:11320/25:10509004 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=4k2._phcCL" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=4k2._phcCL</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10543-025-01089-2" target="_blank" >10.1007/s10543-025-01089-2</a>
Alternative languages
Result language
angličtina
Original language name
On finite precision block Lanczos computations
Original language description
In her seminal 1989 work, Greenbaum demonstrated that the Jacobi matrices produced by the finite precision Lanczos algorithm after k iterations can be interpreted as the results of the exact Lanczos algorithm applied to a larger matrix, whose eigenvalues lie in small intervals around those of the original matrix. This establishes a mathematical model for finite precision Lanczos computations. The present work extends some of these ideas to the block Lanczos algorithm. A generalization of the continuation process is proposed and shown to terminate in a finite number of iterations using carefully constructed perturbations. By deriving sufficient conditions that keep the required perturbations small, it is shown that the eigenvalues of the model matrix stay close to those of the original matrix. While in the single-vector case these conditions are always satisfiable, the question of whether they can always be satisfied in the block case remains open. Finally, numerical experiments demonstrate a practical implementation of the continuation process, empirically assess the validity of the sufficient conditions, and plot the sizes of the perturbations.
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
BIT Numerical Mathematics
ISSN
0006-3835
e-ISSN
1572-9125
Volume of the periodical
65
Issue of the periodical within the volume
November 2025
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
28
Pages from-to
47
UT code for WoS article
001642636500001
EID of the result in the Scopus database
2-s2.0-105021449623