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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Composite convergence bounds based on Chebyshev polynomials and finite precision conjugate gradient computations
Original language description
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
Czech name
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Czech description
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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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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)<br>S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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