On the Numerical Behavior of Matrix Splitting Iteration Methods for Solving Linear Systems

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

On the Numerical Behavior of Matrix Splitting Iteration Methods for Solving Linear Systems

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On the Numerical Behavior of Matrix Splitting Iteration Methods for Solving Linear Systems

Popis výsledku anglicky

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.

Druh

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

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

<a href="/cs/project/GA13-06684S" target="_blank" >GA13-06684S: Iterační metody ve výpočetní matematice: Analýza, předpodmínění a aplikace</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název periodika

SIAM Journal on Numerical Analysis

ISSN

0036-1429

e-ISSN

—

Svazek periodika

53

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

22

Strana od-do

1716-1737

Kód UT WoS článku

000360692100004

EID výsledku v databázi Scopus

2-s2.0-84941066930