Admissible and Attainable Convergence Behavior of Block Arnoldi and GMRES

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68145535%3A_____%2F20%3A00524496" target="_blank" >RIV/68145535:_____/20:00524496 - isvavai.cz</a>

Výsledek na webu

<a href="https://epubs.siam.org/doi/10.1137/19M1272469" target="_blank" >https://epubs.siam.org/doi/10.1137/19M1272469</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/19M1272469" target="_blank" >10.1137/19M1272469</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Admissible and Attainable Convergence Behavior of Block Arnoldi and GMRES

Popis výsledku v původním jazyce

It is well-established that any nonincreasing convergence curve is possible for GMRES and a family of pairs $(A,b)$ can be constructed for which GMRES exhibits a given convergence curve with $A$ having arbitrary spectrum. No analogue of this result has been established for block GMRES, wherein multiple right-hand sides are considered. By reframing the problem as a single linear system over a ring of square matrices, we develop convergence results for block Arnoldi and block GMRES. In particular, we show what convergence behavior is admissible for block GMRES and how the matrices and right-hand sides producing any admissible behavior can be constructed. Moreover, we show that the convergence of the block Arnoldi method for eigenvalue approximation can be almost fully independent of the convergence of block GMRES for the same coefficient matrix and the same starting vectors.nnnn

Název v anglickém jazyce

Admissible and Attainable Convergence Behavior of Block Arnoldi and GMRES

Popis výsledku anglicky

It is well-established that any nonincreasing convergence curve is possible for GMRES and a family of pairs $(A,b)$ can be constructed for which GMRES exhibits a given convergence curve with $A$ having arbitrary spectrum. No analogue of this result has been established for block GMRES, wherein multiple right-hand sides are considered. By reframing the problem as a single linear system over a ring of square matrices, we develop convergence results for block Arnoldi and block GMRES. In particular, we show what convergence behavior is admissible for block GMRES and how the matrices and right-hand sides producing any admissible behavior can be constructed. Moreover, we show that the convergence of the block Arnoldi method for eigenvalue approximation can be almost fully independent of the convergence of block GMRES for the same coefficient matrix and the same starting vectors.nnnn

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/LQ1602" target="_blank" >LQ1602: IT4Innovations excellence in science</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

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

1095-7162

e-ISSN

—

Svazek periodika

41

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

23

Strana od-do

464-486

Kód UT WoS článku

000546981500005

EID výsledku v databázi Scopus

2-s2.0-85084943132