Iterative processes based on block $H$-splittings

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.