On computing quadrature-based bounds for the A-norm of the error in conjugate gradients
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F13%3A00390209" target="_blank" >RIV/67985807:_____/13:00390209 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s11075-012-9591-9" target="_blank" >http://dx.doi.org/10.1007/s11075-012-9591-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11075-012-9591-9" target="_blank" >10.1007/s11075-012-9591-9</a>
Alternative languages
Result language
angličtina
Original language name
On computing quadrature-based bounds for the A-norm of the error in conjugate gradients
Original language description
In their original paper, Golub and Meurant (BIT 37:687?705, 1997) suggest to compute bounds for the A-norm of the error in the conjugate gradient (CG) method using Gauss, Gauss-Radau and Gauss-Lobatto quadratures. The quadratures are computed using the (1,1)-entry of the inverse of the corresponding Jacobi matrix (or its rank-one or rank-two modifications). The resulting algorithm called CGQL computes explicitly the entries of the Jacobi matrix and its modifications from the CG coefficients. In this paper, we use the fact that CG computes the Cholesky decomposition of the Jacobi matrix which is given implicitly. For Gauss-Radau and Gauss-Lobatto quadratures, instead of computing the entries of the modified Jacobi matrices, we directly compute the entries of the Cholesky decompositions of the (modified) Jacobi matrices. This leads to simpler formulas in comparison to those used in CGQL.
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/IAA100300802" target="_blank" >IAA100300802: Theory of Krylov subspace methods and its relationship to other mathematical disciplines</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Numerical Algorithms
ISSN
1017-1398
e-ISSN
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Volume of the periodical
62
Issue of the periodical within the volume
2
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
29
Pages from-to
163-191
UT code for WoS article
000314058700001
EID of the result in the Scopus database
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