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 A is an element of C(pi,n)(m,m) be a weak block H-matrix to partition pi, then for 0 <= r <= omega <= 2/1+rho(vertical bar B(J)(A)vertical bar). rho(B(Lr,omega)) <= vertical bar 1 - omega vertical bar + omega rho(vertical bar B(J)(A)vertical bar), rho(B(Yr,omega)) <= [vertical bar 1 - omega vertical bar + omega rho(vertical bar B(J)(A)vertical bar)](2), 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 (1.999)] and Cvetkovic [Appl. Numer. Math. 41 (2002)] can be improved. (c) 2006 Elsevier Inc. All rights reserved.