Geodesic
Lower bound for the convergence rate of nonstationary Jacobi-like iteration
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 12, pp. 2128-2137
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Stationary and nonstationary Jacobi-like iterative processes for solving systems of linear algebraic equations are examined. For a system whose coefficient matrix $A$ is an $H$-matrix, it is shown that the convergence rate of any Jacobi-like process is at least as high as that of the point Jacobi method as applied to a system with $\langle A\rangle$ as the coefficient matrix, where $\langle A\rangle$ is a comparison matrix of $A$. 
@article{ZVMMF_2006_46_12_a1,
     author = {A. A. Maleev},
     title = {Lower bound for the convergence rate of nonstationary {Jacobi-like} iteration},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2128--2137},
     year = {2006},
     volume = {46},
     number = {12},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_12_a1/}
}
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A. A. Maleev. Lower bound for the convergence rate of nonstationary Jacobi-like iteration. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 12, pp. 2128-2137. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_12_a1/