A convergence analysis of block accelerated over-relaxation iterative methods for weak block H-matrices to partition π

The aim of this paper is to establish the convergence of the block iteration methods such as the block successively accelerated over-relaxation method (BAOR) and the symmetric block successively accelerated over-relaxation method (BSAOR): Let be a weak block H-matrix to partition π, then for , and exact convergence and divergence domains for the block SOR and block SSOR iterative methods are obtained as it has been obtained to H-matrices. Based on these results, the main results in Bai [Parallel Computing 25 (1999)] and Cvetković [Appl. Numer. Math. 41 (2002)] can be improved.