BLOCK KRYLOV SUBSPACE METHODS FOR FUNCTIONS OF MATRICES II: MODIFIED BLOCK FOM
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10421684" target="_blank" >RIV/00216208:11320/20:10421684 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Y6iV5on2qh" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Y6iV5on2qh</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/19M1255847" target="_blank" >10.1137/19M1255847</a>
Alternative languages
Result language
angličtina
Original language name
BLOCK KRYLOV SUBSPACE METHODS FOR FUNCTIONS OF MATRICES II: MODIFIED BLOCK FOM
Original language description
We analyze an expansion of the generalized block Krylov subspace framework of [Electron. Trans. Nurser. Anal., 47 (2017), pp. 100-126]. This expansion allows the use of low-rank modifications of the matrix projected onto the block Krylov subspace and contains, as special cases, the block GMRES method and the new block Radau-Arnoldi method. Within this general setting, we present results that extend the interpolation property from the nonblock case to a matrix polynomial interpolation property for the block case, and we relate the eigenvalues of the projected matrix to the latent roots of these matrix polynomials. Some error bounds for these modified block FOM methods for solving linear systems are presented. We then show how cospatial residuals can be preserved in the case of families of shifted linear block systems. This result is used to derive computationally practical restarted algorithms for block Krylov approximations that compute the action of a matrix function on a set of several vectors simultaneously. We prove some error bounds and present numerical results showing that two modifications of FOM, the block harmonic and the block Radau-Arnoldi methods for matrix functions, can significantly improve the convergence behavior.
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
2020
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
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Volume of the periodical
41
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
34
Pages from-to
804-837
UT code for WoS article
000546981500017
EID of the result in the Scopus database
2-s2.0-85090409673