Conjugate gradients for symmetric positive semidefinite least-squares problems
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F18%3A10240671" target="_blank" >RIV/61989100:27240/18:10240671 - isvavai.cz</a>
Alternative codes found
RIV/61989100:27740/18:10240671
Result on the web
<a href="https://www.tandfonline.com/doi/full/10.1080/00207160.2017.1371701?scroll=top&needAccess=true" target="_blank" >https://www.tandfonline.com/doi/full/10.1080/00207160.2017.1371701?scroll=top&needAccess=true</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1080/00207160.2017.1371701" target="_blank" >10.1080/00207160.2017.1371701</a>
Alternative languages
Result language
angličtina
Original language name
Conjugate gradients for symmetric positive semidefinite least-squares problems
Original language description
The cgSLS (conjugate gradients for symmetric positive semidefinite least-squares) algorithm is presented. The algorithm exploits the cyclic property of invariant Krylov spaces to reduce the least-squares problem with a symmetric positive semidefinite matrix A to the minimization of the related energy function with the Hessian A on the range of A, so that a simple modification of the conjugate gradient (CG) method is applicable. At the same time, the algorithm generates approximations of the projection of the right-hand side to the range of A. The asymptotic rate of convergence of the new algorithm is proved to be the same as that of the CG method for the related consistent problem. An error bound in terms of the square root of the regular condition number of A is also given. The performance of the algorithm is demonstrated by numerical experiments.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
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)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
International Journal of Computer Mathematics
ISSN
1029-0265
e-ISSN
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Volume of the periodical
95
Issue of the periodical within the volume
11
Country of publishing house
GB - UNITED KINGDOM
Number of pages
11
Pages from-to
2229-2239
UT code for WoS article
000441950200005
EID of the result in the Scopus database
2-s2.0-85029436610