Convergence of Inner-Iteration GMRES Methods for Rank-Deficient Least Squares Problems

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F15%3A00438625" target="_blank" >RIV/67985807:_____/15:00438625 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1137/130946009" target="_blank" >http://dx.doi.org/10.1137/130946009</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/130946009" target="_blank" >10.1137/130946009</a>

Result language
angličtina
Original language name
Convergence of Inner-Iteration GMRES Methods for Rank-Deficient Least Squares Problems
Original language description
We develop a general convergence theory for the generalized minimal residual method preconditioned by inner iterations for solving least squares problems. The inner iterations are performed by stationary iterative methods. We also present theoretical justifications for using specific inner iterations such as the Jacobi and SOR-type methods. The theory improves previous work [K. Morikuni and K. Hayami, SIAM J. Matrix Anal. Appl., 34 (2013), pp. 1--22], particularly in the rank-deficient case. We also characterize the spectrum of the preconditioned coefficient matrix by the spectral radius of the iteration matrix for the inner iterations and give a convergence bound for the proposed methods. Finally, numerical experiments show that the proposed methods are more robust and efficient compared to previous methods for some rank-deficient problems.
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
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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