On Error Estimation in the Conjugate Gradient Method and why it Works in Finite Precision Computations.

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F02%3A06020143" target="_blank" >RIV/67985807:_____/02:06020143 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

On Error Estimation in the Conjugate Gradient Method and why it Works in Finite Precision Computations.

Original language description

This paper shows that the lower bound for the A-norm of the error based on Gauss quadrature is mathematically equivalent to the formula given by Hestenes and Stiefel. It compares existing bounds and demonstrates necessity of a proper rounding error analysis. It is given an example of the well-known bound which can fail in finite precision arithmetic. The simplest bound is proved numerically stable. Results are illustrated by numerical experiments.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/GA201%2F02%2F0595" target="_blank" >GA201/02/0595: Mathematical theory of iterative processes with applications</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2002

Confidentiality

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

Name of the periodical

ETNA

ISSN

1068-9613

e-ISSN

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Volume of the periodical

13

Issue of the periodical within the volume

N/A

Country of publishing house

US - UNITED STATES

Number of pages

25

Pages from-to

56-80

UT code for WoS article

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EID of the result in the Scopus database

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