Geodesic
Iterative processes based on block $H$-splittings
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 4, pp. 539-561

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Block $H$-splittings of block square matrices (which, in general, have complex entries) are examined. It is shown that block $H$-matrices are the only ones that admit this type of splittings. Iterative processes corresponding to these splittings are proved to be convergent. The concept of a simple splitting of a block matrix is introduced, and the convergence of iterative processes related to simple splittings of block $H$-matrices is investigated. Multisplitting and nonstationary iterative processes based on block $H$-splittings are considered. Sufficient conditions for their convergence are derived, and some estimates for the asymptotic convergence rate are given. 
@article{ZVMMF_2008_48_4_a0,
     author = {A. A. Maleev},
     title = {Iterative processes based on block $H$-splittings},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {539--561},
     publisher = {mathdoc},
     volume = {48},
     number = {4},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_4_a0/}
}
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A. A. Maleev. Iterative processes based on block $H$-splittings. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 4, pp. 539-561. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_4_a0/