Analysis of the multiplicative Schwarz method for matrices with a special block structure
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10435452" target="_blank" >RIV/00216208:11320/21:10435452 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=OeonpfiKrr" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=OeonpfiKrr</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1553/etna_vol54s31" target="_blank" >10.1553/etna_vol54s31</a>
Alternative languages
Result language
angličtina
Original language name
Analysis of the multiplicative Schwarz method for matrices with a special block structure
Original language description
We analyze the convergence of the (algebraic) multiplicative Schwarz method applied to linear algebraic systems with matrices having a special block structure that arises, for example, when a (partial) differential equation is posed and discretized on a two-dimensional domain that consists of two subdomains with an overlap. This is a basic situation in the context of domain decomposition methods. Our analysis is based on the algebraic structure of the Schwarz iteration matrices, and we derive error bounds that are based on the block diagonal dominance of the given system matrix. Our analysis does not assume that the system matrix is symmetric (positive definite), or has the M-or H-matrix property. Our approach is motivated by, and significantly generalizes, an analysis for a special one-dimensional model problem of Echeverria et al. given in [Electron. Trans. Numer. Anal., 48 (2018), pp. 40-62].
Czech name
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Czech description
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Classification
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
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Electronic Transactions on Numerical Analysis
ISSN
1068-9613
e-ISSN
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Volume of the periodical
54
Issue of the periodical within the volume
November 13, 2020
Country of publishing house
US - UNITED STATES
Number of pages
20
Pages from-to
31-50
UT code for WoS article
000715312600003
EID of the result in the Scopus database
2-s2.0-85097229711