BLOCK KRYLOV SUBSPACE METHODS FOR FUNCTIONS OF MATRICES II: MODIFIED BLOCK FOM

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

BLOCK KRYLOV SUBSPACE METHODS FOR FUNCTIONS OF MATRICES II: MODIFIED BLOCK FOM

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

BLOCK KRYLOV SUBSPACE METHODS FOR FUNCTIONS OF MATRICES II: MODIFIED BLOCK FOM

Popis výsledku anglicky

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.

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

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

0895-4798

e-ISSN

—

Svazek periodika

41

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

34

Strana od-do

804-837

Kód UT WoS článku

000546981500017

EID výsledku v databázi Scopus

2-s2.0-85090409673