Geodesic
On the proving of convergence of multigrid methods
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 4, pp. 5-16

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The paper deals with some problems concerning the proving of convergence of multigrid methods. Special attention is paid to the robust multigrid technique as a variant of geometric multigrid methods with problem-independent transfer operators. The matrix of multigrid iterations is obtained; its norm is estimated. A mesh-independent convergence rate is proved, and a comparison with the classical multigrid methods is performed.
Keywords: geometric multigrid method
Mots-clés : robust multigrid technique, convergence. 
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     author = {S. I. Martynenko},
     title = {On the proving of convergence of multigrid methods},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {5--16},
     publisher = {mathdoc},
     volume = {154},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2012_154_4_a0/}
}
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S. I. Martynenko. On the proving of convergence of multigrid methods. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 4, pp. 5-16. http://geodesic.mathdoc.fr/item/UZKU_2012_154_4_a0/