Composite convergence bounds based on Chebyshev polynomials and finite precision conjugate gradient computations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10173887" target="_blank" >RIV/00216208:11320/14:10173887 - isvavai.cz</a>

Výsledek na webu

<a href="http://link.springer.com/article/10.1007%2Fs11075-013-9713-z" target="_blank" >http://link.springer.com/article/10.1007%2Fs11075-013-9713-z</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11075-013-9713-z" target="_blank" >10.1007/s11075-013-9713-z</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Composite convergence bounds based on Chebyshev polynomials and finite precision conjugate gradient computations

Popis výsledku v původním jazyce

The conjugate gradient method (CG) for solving linear systems of algebraic equations represents a highly nonlinear finite process. Since the original paper of Hestenes and Stiefel published in 1952, it has been linked with the Gauss-Christoffel quadrature approximation of Riemann-Stieltjes distribution functions determined by the data, i.e., with a simplified form of the Stieltjes moment problem. This link, developed further by Vorobyev, Brezinski, Golub, Meurant and others, indicates that a general description of the CG rate of convergence using an asymptotic convergence factor has principal limitations. Moreover, CG is computationally based on short recurrences. In finite precision arithmetic its behaviour is therefore affected by a possible loss oforthogonality among the computed direction vectors. Consequently, any consideration concerning the CG rate of convergence relevant to practical computations must include analysis of effects of rounding errors. Through the example of compo

Název v anglickém jazyce

Composite convergence bounds based on Chebyshev polynomials and finite precision conjugate gradient computations

Popis výsledku anglicky

The conjugate gradient method (CG) for solving linear systems of algebraic equations represents a highly nonlinear finite process. Since the original paper of Hestenes and Stiefel published in 1952, it has been linked with the Gauss-Christoffel quadrature approximation of Riemann-Stieltjes distribution functions determined by the data, i.e., with a simplified form of the Stieltjes moment problem. This link, developed further by Vorobyev, Brezinski, Golub, Meurant and others, indicates that a general description of the CG rate of convergence using an asymptotic convergence factor has principal limitations. Moreover, CG is computationally based on short recurrences. In finite precision arithmetic its behaviour is therefore affected by a possible loss oforthogonality among the computed direction vectors. Consequently, any consideration concerning the CG rate of convergence relevant to practical computations must include analysis of effects of rounding errors. Through the example of compo

Druh

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

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2014

Kód důvěrnosti údajů

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

Název periodika

Numerical Algorithms

ISSN

1017-1398

e-ISSN

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Svazek periodika

65

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

24

Strana od-do

759-782

Kód UT WoS článku

000334172100003

EID výsledku v databázi Scopus

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