Geodesic
On the SOR method with overlapping subsystems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 6, pp. 963-974 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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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