Geodesic
On the SOR method with overlapping subsystems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 6, pp. 963-974 
A. A. Maleev. On the SOR method with overlapping subsystems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 6, pp. 963-974. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_6_a0/
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     title = {On the {SOR} method with overlapping subsystems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {963--974},
     year = {2006},
     volume = {46},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_6_a0/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A description is given of the iterative Jacobi method with overlapping subsystems and the corresponding Gauss–Seidel method. Similarly to the classical case, a generalized SOR method with overlapping subsystems is constructed by introducing an relaxation parameter. The concept of a $\omega$-consistent matrix is defined. It is shown that, with the optimal choice of the parameter, the theory developed by Young remains valid for $\omega$-consistent matrices. This implies certain results for $\omega$-consistent $H$-matrices. The theoretical conclusions obtained in the paper are supported by numerical results.

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