New subclasses of block \(H\)-matrices with applications to parallel decomposition-type relaxation methods (Q857651)

The authors consider parallel decomposition-type relaxation methods [see also \textit{Z. Bai}, Linear Algebra Appl. 282, 1--24 (1998; Zbl 0939.65045) and \textit{Z. Bai} and\textit{Y. Su}, Appl.~Math.~Comput.~81, 1--21 (1997; Zbl 0870.65026)] for solving large systems of linear equations \(AX=B\), where \(A\) is a block \(H\)-matrix. For special subclasses of block \(H\)-matrices \(A\) new sufficient conditions on the relaxation parameters for getting a convergent iterative method are established. The results presented improve the known convergence area for the class of block strictly diagonally dominant matrices.