Konvergence metody GMRES pro třídiagonální Toeplitzovské matice

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F04%3A00103272" target="_blank" >RIV/67985807:_____/04:00103272 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Convergence of GMRES for Tridiagonal Toeplitz Matrices

Popis výsledku v původním jazyce

We analyze the residuals of GMRES, when the method is applied to tridiagonal Toeplitz matrices. We first derive formulas for the residuals as well as their norms when GMRES is applied to scaled Jordan blocks. This problem has been studied previously by Ipsen and Eiermann and Ernst, but we formulate and prove our results in a different way. Intuitively, when a scaled Jordan block is extended to a tridiagonal Toeplitz matrix by a superdiagonal of small modulus (compared to the modulus of the subdiagonal),the GMRES residual norms for both matrices and the same initial residual should be close to each other. We confirm and quantify this intuitive statement. We also demonstrate principal difficulties of any GMRES convergence analysis which is based on eigenvector expansion of the initial residual when the eigenvector matrix is ill-conditioned.

Název v anglickém jazyce

Convergence of GMRES for Tridiagonal Toeplitz Matrices

Popis výsledku anglicky

We analyze the residuals of GMRES, when the method is applied to tridiagonal Toeplitz matrices. We first derive formulas for the residuals as well as their norms when GMRES is applied to scaled Jordan blocks. This problem has been studied previously by Ipsen and Eiermann and Ernst, but we formulate and prove our results in a different way. Intuitively, when a scaled Jordan block is extended to a tridiagonal Toeplitz matrix by a superdiagonal of small modulus (compared to the modulus of the subdiagonal),the GMRES residual norms for both matrices and the same initial residual should be close to each other. We confirm and quantify this intuitive statement. We also demonstrate principal difficulties of any GMRES convergence analysis which is based on eigenvector expansion of the initial residual when the eigenvector matrix is ill-conditioned.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GA201%2F02%2F0595" target="_blank" >GA201/02/0595: Matematická teorie iteračních procesů s aplikacemi</a><br>

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2004

Kód důvěrnosti údajů

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

Název periodika

SIAM Journal on Matrix Analysis and Applications

ISSN

0895-4798

e-ISSN

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Svazek periodika

26

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

19

Strana od-do

233-251

Kód UT WoS článku

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EID výsledku v databázi Scopus

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