THE SHORT-TERM RATIONAL LANCZOS METHOD AND APPLICATIONS

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10455385" target="_blank" >RIV/00216208:11320/22:10455385 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=L7a8FDv6x8" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=L7a8FDv6x8</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/21M1403254" target="_blank" >10.1137/21M1403254</a>

Result language
angličtina
Original language name
THE SHORT-TERM RATIONAL LANCZOS METHOD AND APPLICATIONS
Original language description
Rational Krylov subspaces have become a reference tool in dimension reduction procedures for several application problems. When data matrices are symmetric, a short-term recurrence can be used to generate an associated orthonormal basis. In the past this procedure was abandoned because it requires twice the number of linear system solves per iteration compared with the classical long-term method. We propose an implementation that allows one to obtain the rational subspace reduced matrices at lower overall computational costs than proposed in the literature by also conveniently combining the two system solves. Several applications are discussed where the short-term recurrence feature can be exploited to avoid storing the whole orthonormal basis. We illustrate the advantages of the proposed procedure with several examples.
Czech name
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Czech description
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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

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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