THE SHORT-TERM RATIONAL LANCZOS METHOD AND APPLICATIONS

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

THE SHORT-TERM RATIONAL LANCZOS METHOD AND APPLICATIONS

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

THE SHORT-TERM RATIONAL LANCZOS METHOD AND APPLICATIONS

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

SIAM Journal of Scientific Computing

ISSN

1064-8275

e-ISSN

1095-7197

Svazek periodika

44

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

28

Strana od-do

"A2843"-"A2870"

Kód UT WoS článku

000922908600001

EID výsledku v databázi Scopus

2-s2.0-85140381001