On finite precision block Lanczos computations
Identifikátory výsledku
Kód výsledku v 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>
Výsledek na webu
<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>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
On finite precision block Lanczos computations
Popis výsledku v původním jazyce
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.
Název v anglickém jazyce
On finite precision block Lanczos computations
Popis výsledku anglicky
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.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10102 - Applied mathematics
Návaznosti výsledku
Projekt
—
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Ostatní
Rok uplatnění
2025
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
BIT Numerical Mathematics
ISSN
0006-3835
e-ISSN
1572-9125
Svazek periodika
65
Číslo periodika v rámci svazku
November 2025
Stát vydavatele periodika
NL - Nizozemsko
Počet stran výsledku
28
Strana od-do
47
Kód UT WoS článku
001642636500001
EID výsledku v databázi Scopus
2-s2.0-105021449623