On the Numerical Behavior of Matrix Splitting Iteration Methods for Solving Linear Systems
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F15%3A00444138" target="_blank" >RIV/67985807:_____/15:00444138 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1137/140987936" target="_blank" >http://dx.doi.org/10.1137/140987936</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/140987936" target="_blank" >10.1137/140987936</a>
Alternative languages
Result language
angličtina
Original language name
On the Numerical Behavior of Matrix Splitting Iteration Methods for Solving Linear Systems
Original language description
We study the numerical behavior of stationary one-step or two-step matrix splitting iteration methods for solving large sparse systems of linear equations. We show that inexact solutions of inner linear systems associated with the matrix splittings may considerably influence the accuracy of the approximate solutions computed in finite precision arithmetic. For a general stationary matrix splitting iteration method, we analyze two mathematically equivalent implementations and discuss the conditions whenthey are componentwise or normwise forward or backward stable. We show that a stationary iteration scheme in the residual-updating form is significantly more accurate than in its direct-splitting form when employing inexact inner solves. Theoretical results are illustrated by numerical experiments with the PMHSS method and with the HSS method representing the classes of inexact one-step and two-step splitting iteration methods, respectively.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GA13-06684S" target="_blank" >GA13-06684S: Iterative Methods in Computational Mathematics: Analysis, Preconditioning, and Applications</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SIAM Journal on Numerical Analysis
ISSN
0036-1429
e-ISSN
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Volume of the periodical
53
Issue of the periodical within the volume
4
Country of publishing house
US - UNITED STATES
Number of pages
22
Pages from-to
1716-1737
UT code for WoS article
000360692100004
EID of the result in the Scopus database
2-s2.0-84941066930